Reports emerged this week that Tianjin Teda were interested in the forward, but Sky Tyne and Wear understands he would not consider a move from the north east of England to the north east of China.
A source close to the player insists he is happy at Sunderland and was willing to commit his future to the club, but the Black Cats are now open to offers for the former Paris Saint Germain man.
The source told Sky Tyne and Wear: "He [Sessegnon] has been told he can go.
"He was very happy to commit and stay at Sunderland but if the club wants a clear-out what can you do?"
Work is under way to find the Benin international a new club but a move is not imminent, with the source adding: "At the moment it is quiet."
Sessegnon has scored 18 goals for Sunderland since joining from PSG in 2011 for £6m.