The Black Cats saw a bid rejected by Swansea City for Ayew in the January transfer window and there have been informal discussions over a fresh move for the winger.
It is thought that the Ghanaian is open to leaving the Liberty Stadium and he has tellingly changed agents over recent weeks.
But Ayew wants to join a Champions League club and that could see the uncertainty over his future drag on until the end of the transfer window, with a strong possibility that he will start the season at Swansea.
Sam Allardyce remains a big fan of Ayew and he is keen to bring in reinforcements in the wide attacking roles this summer.
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The Sunderland boss already has Fabio Borini, Wahbi Khazri, Duncan Watmore and Jeremain Lens at his disposal, but the latter is highly likely to depart if the Black Cats receive an acceptable offer.
However, an orthodox central striker is thought to be far more of a priority than any other position, with Diafra Sakho still at the top of Allardyce’s hit-list.
While Ayew has predominantly been used down the middle under Swansea boss Francesco Guidolin, he favours a wide role.
But with Sunderland looking for a new hitman first, it may suit both parties to wait until later in the window to explore a move, with Swansea looking for a fee around the £15million mark.
Sunderland have also been linked with Ayew’s Swansea team-mate, Bafetimbi Gomis, who would be a viable alternative to Sakho, with the French international expected to leave the Welsh club.
Gomis would command a smaller transfer fee than Sakho, albeit he is on a hefty wage at Swansea.
But Marseille appear to be favourites for the 30-year-old, with the French side holding talks over taking him on a season-long loan.