Bayern Munich forward Toni Kroos left the door open for a switch to the Barclays Premier League in the summer.
Tim Sherwood claims the "silence is deafening" from the Tottenham board amid speculation he could be replaced as manager.
The 34-year-old former Fulham, Everton and Manchester United striker has endured a series of injuries since joining the Black Cats last summer.
The former France international has been restricted to just two starts for the first-team, and 14 appearances in total for all competitions.
Saha's release was confirmed shortly after the club completed the signing of Danny Graham from Swansea.
Sunderland chief executive Margaret Byrne said in a statement: "We wish Louis all the very best for the future and thank him for his contribution to Sunderland."
Saha later tweeted: "I can now officially say that SunderlandAfc and I find a mutual agreement to terminate my contract. I want to thank fans, players and staff."