Index: src/wp-admin/js/common.js
===================================================================
--- src/wp-admin/js/common.js	(revision 35153)
+++ src/wp-admin/js/common.js	(working copy)
@@ -246,9 +246,33 @@
 			}
 		}
 
+		currentMenuItemHasPopup();
 		$( document ).trigger( 'wp-collapse-menu', { state: state } );
 	});
 
+	// Handle the `aria-haspopup` attribute on the current menu item when it has a sub-menu.
+	function currentMenuItemHasPopup() {
+		var respWidth,
+			$body = $( document.body ),
+			$current = $( 'a.wp-has-current-submenu' );
+
+		if ( window.innerWidth ) {
+			respWidth = Math.max( window.innerWidth, document.documentElement.clientWidth );
+		} else {
+			respWidth = 961;
+		}
+
+		if ( $body.hasClass( 'folded' ) || ( $body.hasClass( 'auto-fold' ) && respWidth && respWidth <= 960 && respWidth > 782 ) ) {
+			// When folded or auto-folded and not responsive view, the current menu item does have a fly-out sub-menu.
+			$current.attr( 'aria-haspopup', 'true' );
+		} else {
+			// When expanded or in responsive view, reset aria-haspopup.
+			$current.attr( 'aria-haspopup', 'false' );
+		}
+	};
+
+	$document.on( 'wp-window-resized wp-responsive-activate wp-responsive-deactivate', currentMenuItemHasPopup );
+
 	/**
 	 * Ensure an admin submenu is within the visual viewport.
 	 *
@@ -875,6 +899,7 @@
 
 	window.wpResponsive.init();
 	setPinMenu();
+	currentMenuItemHasPopup();
 
 	$document.on( 'wp-pin-menu wp-window-resized.pin-menu postboxes-columnchange.pin-menu postbox-toggled.pin-menu wp-collapse-menu.pin-menu wp-scroll-start.pin-menu', setPinMenu );
 });