The BBC reports that Snodgrass has been told he is surplus to requirements at the London Stadium and can leave the club and Grayson has suggested the Black Cats could make a move.
"When people like him become available, you would be foolish not to consider it", Grayson was quoted as saying by the Northern Echo.
According to Sky Sports, there is just one major catch that will obstruct the deal and that is Sunderland's finances.
That need not concern Sunderland, who need creativity, and Grayson knows the player well, and seems satisfied that he will show the necessary commitment as he seeks to build a team that the Stadium of Light faithful can be proud of again.
The 29-year-old Scotland worldwide has been told he can leave his current club just seven months after his arrival from Hull in a £10.2million deal.
Yet the 29-year-old has failed to impress manager Slaven Bilic and is already being moved on, with Grayson taking interest after missing out on Bournemouth's Max Gradel to Toulouse despite agreeing a deal with the Cherries for the winger.
Robert Snodgrass of West Ham United (L) and Shkodran Mustafi of Arsenal (R) battle for possession.