The Scottish Premier League side have been heavily linked with the Irishman in recent weeks, with reports suggesting they are hoping to seal a year-long temporary move for him.
However, the Black Cats are only interested in a permanent deal for a player who has never been able to establish himself at the Stadium of Light.
Manager Steve Bruce is due to start work on Wearside next week after heading back from his summer break following his appointment last month, and has promised every player in the current squad a chance to prove themselves as he contemplates a fresh recruitment drive.
But that does not appear to extend to the 20-year-old Dubliner, who spent much of last season out on loan, firstly at Sheffield United and then at Crystal Palace.
Stokes, a full Republic of Ireland international, arrived at Sunderland in a £2million switch from Arsenal in January 2007.
He did so having enjoyed a superb spell on loan at Falkirk, where he scored 16 goals in 18 appearances to persuade then manager Roy Keane he had a role to play in his plans for Sunderland.
However, he has managed only five goals in 38 appearances, 22 of them as a substitute, for the Black Cats and found himself behind Kenwyne Jones, Djibril Cisse, Daryl Murphy and David Healy in the pecking order last season.
Hibs' interest in him is understandable - new manager John Hughes was the man who took him to Falkirk, and he is looking for frontmen after selling Steven Fletcher to Burnley.