diff --git a/core/lib/Drupal/Core/Routing/RequestFormatRouteFilter.php b/core/lib/Drupal/Core/Routing/RequestFormatRouteFilter.php
index 8d14dd52cf4c98ac698404da41816819ef67d636..fad7bc04659f0ef4dedc87741a08eae75bfcb79b 100644
--- a/core/lib/Drupal/Core/Routing/RequestFormatRouteFilter.php
+++ b/core/lib/Drupal/Core/Routing/RequestFormatRouteFilter.php
@@ -2,6 +2,7 @@
 
 namespace Drupal\Core\Routing;
 
+use Drupal\Core\Url;
 use Symfony\Component\HttpFoundation\Request;
 use Symfony\Component\HttpKernel\Exception\NotAcceptableHttpException;
 use Symfony\Component\Routing\Route;
@@ -60,7 +61,18 @@ public function filter(RouteCollection $collection, Request $request) {
     // We do not throw a
     // \Symfony\Component\Routing\Exception\ResourceNotFoundException here
     // because we don't want to return a 404 status code, but rather a 406.
-    throw new NotAcceptableHttpException("No route found for the specified format $format.");
+    $available_formats = static::getAvailableFormats($collection);
+    $not_acceptable = new NotAcceptableHttpException("No route found for the specified format $format. Supported formats: " . implode(', ', $available_formats) . '.');
+    if ($available_formats) {
+      $links = [];
+      foreach ($available_formats as $available_format) {
+        $url = Url::fromUri($request->getUri(), ['query' => ['_format' => $available_format]])->toString(TRUE)->getGeneratedUrl();
+        $content_type = $request->getMimeType($available_format);
+        $links[] = "<$url>; rel=\"alternate\"; type=\"$content_type\"";
+      }
+      $not_acceptable->setHeaders(['Link' => implode(', ', $links)]);
+    }
+    throw $not_acceptable;
   }
 
   /**
@@ -79,7 +91,24 @@ public function filter(RouteCollection $collection, Request $request) {
    *   The default format.
    */
   protected static function getDefaultFormat(RouteCollection $collection) {
-    // Get the set of formats across all routes in the collection.
+    $formats = static::getAvailableFormats($collection);
+
+    // The default format is 'html' unless ALL routes require the same format.
+    return count($formats) === 1
+      ? reset($formats)
+      : 'html';
+  }
+
+  /**
+   * Gets the set of formats across all routes in the collection.
+   *
+   * @param \Symfony\Component\Routing\RouteCollection $collection
+   *   The route collection to filter.
+   *
+   * @return string[]
+   *   All available formats.
+   */
+  protected static function getAvailableFormats(RouteCollection $collection) {
     $all_formats = array_reduce($collection->all(), function (array $carry, Route $route) {
       // Routes without a '_format' requirement are assumed to require HTML.
       $route_formats = !$route->hasRequirement('_format')
@@ -87,12 +116,7 @@ protected static function getDefaultFormat(RouteCollection $collection) {
         : explode('|', $route->getRequirement('_format'));
       return array_merge($carry, $route_formats);
     }, []);
-    $formats = array_unique(array_filter($all_formats));
-
-    // The default format is 'html' unless ALL routes require the same format.
-    return count($formats) === 1
-      ? reset($formats)
-      : 'html';
+    return array_unique(array_filter($all_formats));
   }
 
 }
diff --git a/core/modules/rest/tests/src/Functional/EntityResource/EntityResourceTestBase.php b/core/modules/rest/tests/src/Functional/EntityResource/EntityResourceTestBase.php
index 76f0139be75db7684b196c4c9e99f78beb2195e0..6f84d7e131c01ed42eb4aad0bd76ee7ff16189a3 100644
--- a/core/modules/rest/tests/src/Functional/EntityResource/EntityResourceTestBase.php
+++ b/core/modules/rest/tests/src/Functional/EntityResource/EntityResourceTestBase.php
@@ -1492,6 +1492,8 @@ protected function assert406Response(ResponseInterface $response) {
     else {
       // This is the desired response.
       $this->assertSame(406, $response->getStatusCode());
+      $this->stringContains('?_format=' . static::$format . '>; rel="alternate"; type="' . static::$mimeType . '"', $response->getHeader('Link'));
+      $this->stringContains('?_format=foobar>; rel="alternate"', $response->getHeader('Link'));
     }
   }
 
diff --git a/core/tests/Drupal/Tests/Core/Routing/RequestFormatRouteFilterTest.php b/core/tests/Drupal/Tests/Core/Routing/RequestFormatRouteFilterTest.php
index 3574ee195004ca24718284846eefd19e9f4341c9..83d0505f15c765a2dbf3d4af011c2d2a9cb7ca81 100644
--- a/core/tests/Drupal/Tests/Core/Routing/RequestFormatRouteFilterTest.php
+++ b/core/tests/Drupal/Tests/Core/Routing/RequestFormatRouteFilterTest.php
@@ -2,7 +2,10 @@
 
 namespace Drupal\Tests\Core\Routing;
 
+use Drupal\Core\DependencyInjection\ContainerBuilder;
+use Drupal\Core\GeneratedUrl;
 use Drupal\Core\Routing\RequestFormatRouteFilter;
+use Drupal\Core\Utility\UnroutedUrlAssemblerInterface;
 use Drupal\Tests\UnitTestCase;
 use Symfony\Component\HttpFoundation\Request;
 use Symfony\Component\HttpKernel\Exception\NotAcceptableHttpException;
@@ -59,6 +62,14 @@ public function filterProvider() {
    * @covers ::filter
    */
   public function testNoRouteFound() {
+    $url = $this->prophesize(GeneratedUrl::class);
+    $url_assembler = $this->prophesize(UnroutedUrlAssemblerInterface::class);
+    $url_assembler->assemble('http://localhost/test?_format=xml', ['query' => ['_format' => 'json'], 'external' => TRUE], TRUE)
+      ->willReturn($url);
+    $container = new ContainerBuilder();
+    $container->set('unrouted_url_assembler', $url_assembler->reveal());
+    \Drupal::setContainer($container);
+
     $collection = new RouteCollection();
     $route_with_format = $route = new Route('/test');
     $route_with_format->setRequirement('_format', 'json');
@@ -78,6 +89,16 @@ public function testNoRouteFound() {
   public function testNoRouteFoundWhenNoRequestFormatAndSingleRouteWithMultipleFormats() {
     $this->setExpectedException(NotAcceptableHttpException::class, 'No route found for the specified format html.');
 
+    $url = $this->prophesize(GeneratedUrl::class);
+    $url_assembler = $this->prophesize(UnroutedUrlAssemblerInterface::class);
+    $url_assembler->assemble('http://localhost/test', ['query' => ['_format' => 'json'], 'external' => TRUE], TRUE)
+      ->willReturn($url);
+    $url_assembler->assemble('http://localhost/test', ['query' => ['_format' => 'xml'], 'external' => TRUE], TRUE)
+      ->willReturn($url);
+    $container = new ContainerBuilder();
+    $container->set('unrouted_url_assembler', $url_assembler->reveal());
+    \Drupal::setContainer($container);
+
     $collection = new RouteCollection();
     $route_with_format = $route = new Route('/test');
     $route_with_format->setRequirement('_format', 'json|xml');