The Welsh winger, 34, is out-of-contract at the end of next season - and at 34-years-old, it remains to be seen whether he would be offered a new deal.
The People says Giggs has received some grief from sections of the Man United crowd in recent weeks.
Any chance of this deal materialising could be scuppered by the midfielder's £70,000-a-week demands.
Sunderland already have 4 left-sided midfielders on their books - Daryl Muprhy; Ross Wallace; Andy Reid and Kieran Richardson have all played a part in that position this season. However, the chance to sign a superstar like Giggs doesn't come around too often so it is unlikely that the Sunderland boss would pass up the chance to sign his former team-mate.