The young midfielder has been linked with the Black Cats and Championship side Blackburn Rovers this summer, with other sides south of the border understood to be monitoring the situation.
Ross, 19, spent time last season on loan at Scottish Championship outfit Raith Rovers and had been expected to challenge for a first-team place at Pittodrie this season.
He was offered fresh terms by the Dons, but The Press & Journal now report that Aberdeen boss Stephen Glass is resigned to losing the winger after he informed the club that he would not be returning for pre-season.
That could open the door for Sunderland to make their move – although compensation will be required when Ross finds a new club given his age.
The Wearsiders are yet to secure a signing during the window, but are working hard on a number of fronts behind the scenes.