diff -u b/core/modules/update/src/ProjectCoreCompatibility.php b/core/modules/update/src/ProjectCoreCompatibility.php
--- b/core/modules/update/src/ProjectCoreCompatibility.php
+++ b/core/modules/update/src/ProjectCoreCompatibility.php
@@ -139,6 +139,9 @@
     foreach ($releases_to_set as &$release) {
       if (!empty($release['core_compatibility'])) {
         $release['core_compatible'] = $this->isCoreCompatible($release['core_compatibility']);
+        if (!$release['core_compatible']) {
+          $release['hide_download_link'] = TRUE;
+        }
         $release['core_compatibility_range'] = $this->createMessageFromCoreCompatibility($release['core_compatibility']);
         $release['core_compatibility_details'] = $this->createCoreCompatibilityDetails($release['core_compatible'], $release['core_compatibility_range']);
       }
diff -u b/core/modules/update/templates/update-version.html.twig b/core/modules/update/templates/update-version.html.twig
--- b/core/modules/update/templates/update-version.html.twig
+++ b/core/modules/update/templates/update-version.html.twig
@@ -13,6 +13,7 @@
  *   - release_link: The URL for the release notes.
  *   - core_compatible (bool): Is it compatible with the installed core or not?
  *   - core_compatibility_details: Render array of core compatibility details.
+ *   - hide_download_link (bool|NULL): Should the download link be hidden?
  *
  * @ingroup themeable
  */
@@ -26,7 +27,7 @@
     </div>
     <div class="layout-column layout-column--half">
       <ul class="project-update__version-links">
-        {% if version.show_download_link %}
+        {% if version.hide_download_link is empty %}
           <li class="project-update__download-link">
             <a href="{{ version.download_link }}">{{ 'Download'|t }}</a>
           </li>
reverted:
--- b/core/modules/update/update.report.inc
+++ a/core/modules/update/update.report.inc
@@ -114,14 +114,6 @@
   // Storing by reference because we are sorting the project values.
   $project = &$variables['project'];
 
-  $set_download_link_flag = function (&$version) use ($project) {
-    if ($project['name'] === 'drupal' || !empty($version['core_compatible'])) {
-      $version['show_download_link'] = TRUE;
-      return;
-    }
-    $version['show_download_link'] = FALSE;
-  };
-
   // Set the project title and URL.
   $variables['title'] = (isset($project['title'])) ? $project['title'] : $project['name'];
   $variables['url'] = (isset($project['link'])) ? Url::fromUri($project['link'])->toString() : NULL;
@@ -165,7 +157,6 @@
         ) {
           $version_class[] = 'project-update__version--recommended-strong';
         }
-        $set_download_link_flag($project['releases'][$project['recommended']]);
         $versions_inner[] = [
           '#theme' => 'update_version',
           '#version' => $project['releases'][$project['recommended']],
@@ -178,7 +169,6 @@
       if (!empty($project['security updates'])) {
         $security_class[] = 'version-security';
         foreach ($project['security updates'] as $security_update) {
-          $set_download_link_flag($security_update);
           $versions_inner[] = [
             '#theme' => 'update_version',
             '#version' => $security_update,
@@ -190,7 +180,6 @@
     }
 
     if ($project['recommended'] !== $project['latest_version']) {
-      $set_download_link_flag($project['releases'][$project['latest_version']]);
       $versions_inner[] = [
         '#theme' => 'update_version',
         '#version' => $project['releases'][$project['latest_version']],
@@ -202,7 +191,6 @@
       && $project['status'] != UpdateManagerInterface::CURRENT
       && isset($project['dev_version'])
       && $project['recommended'] !== $project['dev_version']) {
-      $set_download_link_flag($project['releases'][$project['dev_version']]);
       $versions_inner[] = [
         '#theme' => 'update_version',
         '#version' => $project['releases'][$project['dev_version']],
@@ -214,7 +202,6 @@
 
   if (isset($project['also'])) {
     foreach ($project['also'] as $also) {
-      $set_download_link_flag($project['releases'][$also]);
       $versions_inner[] = [
         '#theme' => 'update_version',
         '#version' => $project['releases'][$also],
diff -u b/core/themes/claro/templates/admin/update-version.html.twig b/core/themes/claro/templates/admin/update-version.html.twig
--- b/core/themes/claro/templates/admin/update-version.html.twig
+++ b/core/themes/claro/templates/admin/update-version.html.twig
@@ -13,6 +13,7 @@
  *   - release_link: The URL for the release notes.
  *   - core_compatible (bool): Is it compatible with the installed core or not?
  *   - core_compatibility_details: Render array of core compatibility details.
+ *   - hide_download_link (bool|NULL): Should the download link be hidden?
  */
 #}
 <div class="{{ attributes.class }} project-update__version"{{ attributes|without('class') }}>
@@ -24,7 +25,7 @@
     </div>
     <div class="layout-column layout-column--half">
       <ul class="project-update__version-links">
-        {% if version.show_download_link %}
+        {% if version.hide_download_link is empty %}
           <li class="project-update__download-link">
             <a href="{{ version.download_link }}">{{ 'Download'|t }}</a>
           </li>
diff -u b/core/themes/stable/templates/admin/update-version.html.twig b/core/themes/stable/templates/admin/update-version.html.twig
--- b/core/themes/stable/templates/admin/update-version.html.twig
+++ b/core/themes/stable/templates/admin/update-version.html.twig
@@ -13,6 +13,7 @@
  *   - release_link: The URL for the release notes.
  *   - core_compatible (bool): Is it compatible with the installed core or not?
  *   - core_compatibility_details: Render array of core compatibility details.
+ *   - hide_download_link (bool|NULL): Should the download link be hidden?
  */
 #}
 <div class="{{ attributes.class }} project-update__version"{{ attributes|without('class') }}>
@@ -24,7 +25,7 @@
     </div>
     <div class="layout-column layout-column--half">
       <ul class="project-update__version-links">
-        {% if version.show_download_link %}
+        {% if version.hide_download_link is empty %}
           <li class="project-update__download-link">
             <a href="{{ version.download_link }}">{{ 'Download'|t }}</a>
           </li>