The Black Cats snapped up centre back Sebastian Coates on a permanent deal from Liverpool last week, before purchasing Celtic right back Adam Matthews on Friday.
Now, manager Dick Advocaat needs to look towards the final third, with attacking reinforcements certainly needed if Sunderland are to improve on last season's struggles.
The Mirror believe that, with Georginio Wijnaldum preferring a move to Newcastle, Advocaat has turned his attention towards Everton's McGeady, who could be out of favour after the Toffees landed Barcelona's Gerard Deulofeu.
The Irish international could look to leave Goodison Park this summer, and whilst the Liverpool Echo recently reported that a move back to former club Celtic could be on the cards, Sunderland are reportedly hoping to keep him in the Premier League.
Celtic or Sunderland?
The prospect of staying in the Premier League could be appealing to the 29-year-old, but with his Everton future in doubt, he would certainly need guarantees over his playing time in order to move to Sunderland.
Whereas with Celtic, McGeady would be returning as a star having dazzled for the club previously, and Ronny Deila's men can also offer Champions League football.
If McGeady has to decide between the two, it could come down to head vs heart, as he chooses between staying in the Premier League or returning to the club where he made his name - and the latter could well win out at this stage of his career.