The club are resigned to losing Dick Advocaat at the end of the campaign as the Dutchman is set to retire from football, and so Sunderland bosses are already looking for a new man to take the hot seat at the Stadium of Light next term.
Moyes is seen as an ideal candidate for the job if the Black Cats can convince him to leave Spanish side Real Sociedad after just one season.
The Scottish coach joined Sociedad in November and will see his team finish 12th in his first campaign in Spanish football, but could be tempted by an offer to return to the Premier League with Sunderland.
Any choice will depend on whether the Wearsiders retain their Premier League status next year as there is still a chance they will be relegated, but that is unlikely, and so Moyes could be approached soon.
Sources close to the former United boss have reportedly said there has not been any contact from the Black Cats but an approach is expected in the coming months.
Would David Moyes be a good appointment as Sunderland manager? Should he return to the Premier League?