diff --git a/core/modules/update/src/UpdateFetcher.php b/core/modules/update/src/UpdateFetcher.php
index 2b03c9c101..05cce763a6 100644
--- a/core/modules/update/src/UpdateFetcher.php
+++ b/core/modules/update/src/UpdateFetcher.php
@@ -77,7 +77,7 @@ public function fetchProjectData(array $project, $site_key = '') {
   public function buildFetchUrl(array $project, $site_key = '') {
     $name = $project['name'];
     $url = $this->getFetchBaseUrl($project);
-    $url .= '/' . $name . '/' . \Drupal::CORE_COMPATIBILITY;
+    $url .= '/' . $name . '/current';
 
     // Only append usage information if we have a site key and the project is
     // enabled. We do not want to record usage statistics for disabled projects.
diff --git a/core/modules/update/src/UpdateProjectCoreCompatibility.php b/core/modules/update/src/UpdateProjectCoreCompatibility.php
new file mode 100644
index 0000000000..0a57ace24c
--- /dev/null
+++ b/core/modules/update/src/UpdateProjectCoreCompatibility.php
@@ -0,0 +1,127 @@
+<?php
+
+namespace Drupal\update;
+
+use Composer\Semver\Semver;
+use Composer\Semver\VersionParser;
+
+/**
+ * Utility class to set core compatibility ranges.
+ */
+class UpdateProjectCoreCompatibility {
+
+  /**
+   * Set core_compatibility_ranges for project releases.
+   *
+   * @todo Update Security releases also.
+   * @todo update core/modules/update/templates/update-version.html.twig to
+   *   output the ranges.
+   * @param array &$project_data
+   * @param array $available_project
+   * @param array $available_core
+   */
+  public static function setProjectCoreCompatibilityRanges(array $project_data, array &$project_releases, $core_data, array $core_releases) {
+    if (!isset($core_data['existing_version']) || !isset($core_releases[$core_data['existing_version']])) {
+      // If we can't determine the existing version then we can't calculate
+      // the core compatibility of based on core versions after the existing
+      // versions.
+      return;
+    }
+    $releases_to_set = [];
+    $possible_core_update_versions = self::getPossibleCoreUpdateVersions($core_data, $core_releases);
+      foreach (['recommended', 'latest_version'] as $update_version_type) {
+      if (isset($project_data[$update_version_type])&& !empty($project_releases[$project_data[$update_version_type]])) {
+        $releases_to_set[] = &$project_releases[$project_data[$update_version_type]];
+      }
+    }
+    if (!empty($project_data['also'])) {
+      foreach ($project_data['also'] as $version) {
+        if (isset($project_releases[$version])) {
+          $releases_to_set[] = &$project_releases[$version];
+        }
+      }
+    }
+    foreach ($releases_to_set as &$release) {
+      if (!empty($release['core_compatibility'])) {
+        $release['core_compatibility_ranges'] = self::createCompatibilityRanges($release['core_compatibility'], $possible_core_update_versions);
+        if ($release['core_compatibility_ranges']) {
+          $release['core_compatibility_message'] = self::formatMessage($release['core_compatibility_ranges']);
+        }
+      }
+
+    }
+
+  }
+
+  /**
+   * @param $core_data
+   * @param array $core_releases
+   *
+   * @return array
+   */
+  protected static function getPossibleCoreUpdateVersions($core_data, array $core_releases) {
+    $core_release_versions = array_keys($core_releases);
+    $possible_core_update_versions = Semver::satisfiedBy($core_release_versions, '>= ' . $core_data['existing_version']);
+    $possible_core_update_versions = Semver::sort($possible_core_update_versions);
+    $possible_core_update_versions = array_filter($possible_core_update_versions, function ($version) {
+      return VersionParser::parseStability($version) === 'stable';
+    });
+    return $possible_core_update_versions;
+  }
+
+  /**
+   * @param $core_compatibility
+   * @param array $possible_core_update_versions
+   *
+   * @return array
+   */
+  protected static function createCompatibilityRanges($core_compatibility, array $possible_core_update_versions) {
+    // @todo statically cache the results here because this will the same for many projects
+    // because they will likely use the same core_compatibility.
+    // For example "^8 || ^9" or "^8.8 || ^9" should be very common.
+    $compatibility_ranges = [];
+    $previous_version_satisfied = NULL;
+    $range = [];
+    foreach ($possible_core_update_versions as $possible_core_update_version) {
+      if (Semver::satisfies($possible_core_update_version, $core_compatibility)) {
+        if (empty($range)) {
+          $range[] = $possible_core_update_version;
+        }
+        else {
+          $range[1] = $possible_core_update_version;
+        }
+
+      }
+      else {
+        if ($range) {
+          if ($previous_version_satisfied) {
+            // Make the previous version be the second item in the current
+            // range.
+            $range[] = $previous_version_satisfied;
+          }
+          $compatibility_ranges[] = $range;
+        }
+        // Start a new range.
+        $range = [];
+      }
+
+    }
+    if ($range) {
+      $compatibility_ranges[] = $range;
+    }
+    return $compatibility_ranges;
+  }
+
+  protected static function formatMessage(array $core_compatibility_ranges) {
+    $range_messages = [];
+    foreach ($core_compatibility_ranges as $core_compatibility_range) {
+      $range_message = $core_compatibility_range[0];
+      if (count($core_compatibility_range) === 2) {
+        $range_message .= " to {$core_compatibility_range[1]}";
+      }
+      $range_messages[] = $range_message;
+    }
+    return t('This module is compatible with Drupal core:') . ' ' . implode(', ', $range_messages);
+  }
+
+}
diff --git a/core/modules/update/templates/update-version.html.twig b/core/modules/update/templates/update-version.html.twig
index c21c4f0ba4..38587d1ab4 100644
--- a/core/modules/update/templates/update-version.html.twig
+++ b/core/modules/update/templates/update-version.html.twig
@@ -21,6 +21,9 @@
     <div class="project-update__version-details layout-column layout-column--quarter">
       <a href="{{ version.release_link }}">{{ version.version }}</a>
       <span class="project-update__version-date">({{ version.date|date('Y-M-d') }})</span>
+      {% if version.core_compatibility_message %}
+        <span>{{ version.core_compatibility_message }}</span>
+      {% endif %}
     </div>
     <div class="layout-column layout-column--half">
       <ul class="project-update__version-links">
diff --git a/core/modules/update/tests/src/Unit/UpdateFetcherTest.php b/core/modules/update/tests/src/Unit/UpdateFetcherTest.php
index 61c767deda..fb06f4173e 100644
--- a/core/modules/update/tests/src/Unit/UpdateFetcherTest.php
+++ b/core/modules/update/tests/src/Unit/UpdateFetcherTest.php
@@ -5,10 +5,6 @@
 use Drupal\Tests\UnitTestCase;
 use Drupal\update\UpdateFetcher;
 
-if (!defined('DRUPAL_CORE_COMPATIBILITY')) {
-  define('DRUPAL_CORE_COMPATIBILITY', '8.x');
-}
-
 /**
  * Tests update functionality unrelated to the database.
  *
@@ -71,20 +67,20 @@ public function providerTestUpdateBuildFetchUrl() {
     $project['info']['project status url'] = 'http://www.example.com';
     $project['includes'] = ['module1' => 'Module 1', 'module2' => 'Module 2'];
     $site_key = '';
-    $expected = 'http://www.example.com/' . $project['name'] . '/' . DRUPAL_CORE_COMPATIBILITY;
+    $expected = 'http://www.example.com/' . $project['name'] . '/current';
 
     $data[] = [$project, $site_key, $expected];
 
     // For disabled projects it shouldn't add the site key either.
     $site_key = 'site_key';
     $project['project_type'] = 'disabled';
-    $expected = 'http://www.example.com/' . $project['name'] . '/' . DRUPAL_CORE_COMPATIBILITY;
+    $expected = 'http://www.example.com/' . $project['name'] . '/current';
 
     $data[] = [$project, $site_key, $expected];
 
     // For enabled projects, test adding the site key.
     $project['project_type'] = '';
-    $expected = 'http://www.example.com/' . $project['name'] . '/' . DRUPAL_CORE_COMPATIBILITY;
+    $expected = 'http://www.example.com/' . $project['name'] . '/current';
     $expected .= '?site_key=site_key';
     $expected .= '&list=' . rawurlencode('module1,module2');
 
@@ -92,7 +88,7 @@ public function providerTestUpdateBuildFetchUrl() {
 
     // Test when the URL contains a question mark.
     $project['info']['project status url'] = 'http://www.example.com/?project=';
-    $expected = 'http://www.example.com/?project=/' . $project['name'] . '/' . DRUPAL_CORE_COMPATIBILITY;
+    $expected = 'http://www.example.com/?project=/' . $project['name'] . '/current';
     $expected .= '&site_key=site_key';
     $expected .= '&list=' . rawurlencode('module1,module2');
 
diff --git a/core/modules/update/tests/src/Unit/UpdateProjectCoreCompatibilityTest.php b/core/modules/update/tests/src/Unit/UpdateProjectCoreCompatibilityTest.php
new file mode 100644
index 0000000000..fc49bfc2c7
--- /dev/null
+++ b/core/modules/update/tests/src/Unit/UpdateProjectCoreCompatibilityTest.php
@@ -0,0 +1,143 @@
+<?php
+
+namespace Drupal\Tests\update\Unit;
+
+use Drupal\Tests\UnitTestCase;
+use Drupal\update\UpdateProjectCoreCompatibility;
+
+/**
+ * @coversDefaultClass \Drupal\update\UpdateProjectCoreCompatibility
+ *
+ * @group update
+ */
+class UpdateProjectCoreCompatibilityTest extends UnitTestCase {
+
+  /**
+   * @covers ::setProjectCoreCompatibilityRanges
+   * @dataProvider providerSetProjectCoreCompatibilityRanges
+   */
+  public function testSetProjectCoreCompatibilityRanges(array $project_data, array $project_releases, $core_data, array $core_releases, array $expected_releases) {
+    UpdateProjectCoreCompatibility::setProjectCoreCompatibilityRanges($project_data, $project_releases, $core_data, $core_releases);
+    $this->assertSame($expected_releases, $project_releases);
+  }
+
+  /**
+   * Dataprovider for testSetProjectCoreCompatibilityRanges().
+   */
+  public function providerSetProjectCoreCompatibilityRanges() {
+    $test_cases['no 9 releases'] = [
+      'project_data' => [
+        'recommended' => '1.0.1',
+        'latest_version' => '1.2.3',
+        'also' => [
+          '1.2.4',
+          '1.2.5',
+          '1.2.6',
+        ],
+      ],
+      'project_releases' => [
+        '1.0.1' => [
+          'core_compatibility' => '^8.8 || ^9',
+        ],
+        '1.2.3' => [
+          'core_compatibility' => '^8.9 || ^9',
+        ],
+        '1.2.4' => [
+          'core_compatibility' => '^8.9.2 || ^9',
+        ],
+        '1.2.5' => [
+          'core_compatibility' => '8.9.0 || 8.9.2 || ^9.0.1',
+        ],
+        '1.2.6' => [],
+      ],
+      'core_data' => [
+        'existing_version' => '8.8.0',
+      ],
+      'core_releases' => [
+        '8.8.0-alpha1' => [],
+        '8.8.0-beta1' => [],
+        '8.8.0-rc1' => [],
+        '8.8.0' => [],
+        '8.8.1' => [],
+        '8.8.2' => [],
+        '8.9.0' => [],
+        '8.9.1' => [],
+        '8.9.2' => [],
+      ],
+      'expected_releases' => [
+        '1.0.1' => [
+          'core_compatibility' => '^8.8 || ^9',
+          'core_compatibility_ranges' => [['8.8.0', '8.9.2']],
+          'core_compatibility_message' => 'This module is compatible with Drupal core: 8.8.0 to 8.9.2',
+        ],
+        '1.2.3' => [
+          'core_compatibility' => '^8.9 || ^9',
+          'core_compatibility_ranges' => [['8.9.0', '8.9.2']],
+          'core_compatibility_message' => 'This module is compatible with Drupal core: 8.9.0 to 8.9.2',
+        ],
+        '1.2.4' => [
+          'core_compatibility' => '^8.9.2 || ^9',
+          'core_compatibility_ranges' => [['8.9.2']],
+          'core_compatibility_message' => 'This module is compatible with Drupal core: 8.9.2',
+        ],
+        '1.2.5' => [
+          'core_compatibility' => '8.9.0 || 8.9.2 || ^9.0.1',
+          'core_compatibility_ranges' => [['8.9.0'], ['8.9.2']],
+          'core_compatibility_message' => 'This module is compatible with Drupal core: 8.9.0, 8.9.2',
+        ],
+        '1.2.6' => [],
+      ],
+    ];
+    // Ensure that when only Drupal 9 pre-releases none of the expected ranges
+    // change.
+    $test_cases['with 9 pre releases'] = $test_cases['no 9 releases'];
+    $test_cases['with 9 pre releases']['core_releases'] += [
+      '9.0.0-alpha1' => [],
+      '9.0.0-beta1' => [],
+      '9.0.0-rc1' => [],
+    ];
+    // Ensure that when the Drupal 9 full release are added the expected ranges
+    // do change.
+    $test_cases['with 9 full releases'] = $test_cases['with 9 pre releases'];
+    $test_cases['with 9 full releases']['core_releases'] += [
+      '9.0.0' => [],
+      '9.0.1' => [],
+      '9.0.2' => [],
+    ];
+    $test_cases['with 9 full releases']['expected_releases'] = [
+      '1.0.1' => [
+        'core_compatibility' => '^8.8 || ^9',
+        'core_compatibility_ranges' => [['8.8.0', '9.0.2']],
+        'core_compatibility_message' => 'This module is compatible with Drupal core: 8.8.0 to 9.0.2',
+      ],
+      '1.2.3' => [
+        'core_compatibility' => '^8.9 || ^9',
+        'core_compatibility_ranges' => [['8.9.0', '9.0.2']],
+        'core_compatibility_message' => 'This module is compatible with Drupal core: 8.9.0 to 9.0.2',
+      ],
+      '1.2.4' => [
+        'core_compatibility' => '^8.9.2 || ^9',
+        'core_compatibility_ranges' => [['8.9.2', '9.0.2']],
+        'core_compatibility_message' => 'This module is compatible with Drupal core: 8.9.2 to 9.0.2',
+      ],
+      '1.2.5' => [
+        'core_compatibility' => '8.9.0 || 8.9.2 || ^9.0.1',
+        'core_compatibility_ranges' => [['8.9.0'], ['8.9.2'], ['9.0.1', '9.0.2']],
+        'core_compatibility_message' => 'This module is compatible with Drupal core: 8.9.0, 8.9.2, 9.0.1 to 9.0.2',
+      ],
+      '1.2.6' => [],
+    ];
+    return $test_cases;
+  }
+
+}
+
+namespace Drupal\update;
+
+if (!function_exists('t')) {
+
+  function t($string, array $args = []) {
+    return strtr($string, $args);
+  }
+
+}
diff --git a/core/modules/update/update.compare.inc b/core/modules/update/update.compare.inc
index dd658120ef..373f38682f 100644
--- a/core/modules/update/update.compare.inc
+++ b/core/modules/update/update.compare.inc
@@ -5,6 +5,8 @@
  * Code required only when comparing available updates to existing data.
  */
 
+use Drupal\update\UpdateProjectCoreCompatibility;
+
 /**
  * Determines version and type information for currently installed projects.
  *
@@ -90,9 +92,20 @@ function update_calculate_project_data($available) {
   }
   $projects = \Drupal::service('update.manager')->getProjects();
   update_process_project_info($projects);
+  $drupal_project_info = NULL;
+  if (isset($projects['drupal']) && !empty($available['drupal']['releases'])) {
+    $drupal_project_info = $projects['drupal'];
+    unset($projects['drupal']);
+    $projects = array_merge(['drupal' => $drupal_project_info], $projects);
+  }
+
   foreach ($projects as $project => $project_info) {
     if (isset($available[$project])) {
       update_calculate_project_update_status($projects[$project], $available[$project]);
+      if ($drupal_project_info && $project !== 'drupal' && !empty($available[$project]['releases'])) {
+        UpdateProjectCoreCompatibility::setProjectCoreCompatibilityRanges($projects[$project], $available[$project]['releases'], $projects['drupal'], $available['drupal']['releases']);
+      }
+
     }
     else {
       $projects[$project]['status'] = UPDATE_UNKNOWN;