diff --git a/src/wp-includes/rest-api/endpoints/class-wp-rest-attachments-controller.php b/src/wp-includes/rest-api/endpoints/class-wp-rest-attachments-controller.php
index 589e0e2ccec17..53b94bf43947b 100644
--- a/src/wp-includes/rest-api/endpoints/class-wp-rest-attachments-controller.php
+++ b/src/wp-includes/rest-api/endpoints/class-wp-rest-attachments-controller.php
@@ -970,6 +970,33 @@ public function prepare_item_for_response( $item, $request ) {
 		return apply_filters( 'rest_prepare_attachment', $response, $post, $request );
 	}
 
+	/**
+	 * Prepares attachment links for the request.
+	 *
+	 * @since 6.9.0
+	 *
+	 * @param WP_Post $post Post object.
+	 * @return array Links for the given attachment.
+	 */
+	protected function prepare_links( $post ) {
+		$links = parent::prepare_links( $post );
+
+		if ( ! empty( $post->post_parent ) ) {
+			$post = get_post( $post->post_parent );
+
+			if ( ! empty( $post ) ) {
+				$links['post'] = array(
+					'href'       => rest_url( rest_get_route_for_post( $post ) ),
+					'embeddable' => true,
+					'post_type'  => $post->post_type,
+					'id'         => $post->ID,
+				);
+			}
+		}
+
+		return $links;
+	}
+
 	/**
 	 * Retrieves the attachment's schema, conforming to JSON Schema.
 	 *
diff --git a/tests/phpunit/tests/rest-api/rest-attachments-controller.php b/tests/phpunit/tests/rest-api/rest-attachments-controller.php
index d065238b8beb7..3bc9f798e6d7e 100644
--- a/tests/phpunit/tests/rest-api/rest-attachments-controller.php
+++ b/tests/phpunit/tests/rest-api/rest-attachments-controller.php
@@ -1848,12 +1848,54 @@ public function test_links_exist() {
 
 		$this->assertArrayHasKey( 'self', $links );
 		$this->assertArrayHasKey( 'author', $links );
+		$this->assertArrayNotHasKey( 'post', $links );
 
 		$this->assertCount( 1, $links['author'] );
 		$this->assertArrayHasKey( 'embeddable', $links['author'][0]['attributes'] );
 		$this->assertTrue( $links['author'][0]['attributes']['embeddable'] );
 	}
 
+	/**
+	 * @ticket 64034
+	 */
+	public function test_links_contain_parent() {
+		wp_set_current_user( self::$editor_id );
+
+		$post       = self::factory()->post->create(
+			array(
+				'post_type'   => 'post',
+				'post_status' => 'publish',
+				'post_title'  => 'Test Post',
+			)
+		);
+		$attachment = self::factory()->attachment->create_object(
+			array(
+				'file'           => self::$test_file,
+				'post_author'    => self::$editor_id,
+				'post_parent'    => $post,
+				'post_mime_type' => 'image/jpeg',
+			)
+		);
+
+		$this->assertGreaterThan( 0, $attachment );
+
+		$request = new WP_REST_Request( 'GET', "/wp/v2/media/{$attachment}" );
+		$request->set_query_params( array( 'context' => 'edit' ) );
+
+		$response = rest_get_server()->dispatch( $request );
+		$links    = $response->get_links();
+
+		$this->assertArrayHasKey( 'self', $links );
+		$this->assertArrayHasKey( 'author', $links );
+		$this->assertArrayHasKey( 'post', $links );
+
+		$this->assertCount( 1, $links['author'] );
+		$this->assertSame( rest_url( '/wp/v2/posts/' . $post ), $links['post'][0]['href'] );
+		$this->assertSame( 'post', $links['post'][0]['attributes']['post_type'] );
+		$this->assertSame( $post, $links['post'][0]['attributes']['id'] );
+		$this->assertTrue( $links['post'][0]['attributes']['embeddable'] );
+	}
+
 	public function test_publish_action_ldo_not_registered() {
 
 		$response = rest_get_server()->dispatch( new WP_REST_Request( 'OPTIONS', '/wp/v2/media' ) );