The 28-year-old is set to be out of contract in a few months’ time, and is rumoured to be willing to leave the North East even if the Black Cats can avoid relegation.
Stoke are particularly keen on the Swede, and are ready to offer him a fresh challenge.
Potters chief Mark Hughes is known to be eager to distance his side from the direct football they have been associated with for some time, and sees the technically adept Swede as a good player to impose his philosophy.
Larsson is also rumoured to be attracting interest from German sides, yet staying in the Premier League may be more appealing to the former Arsenal trainee.
Sunderland also face the prospect of losing other big name players.
Fellow midfielder Jack Colback is wanted by Newcastle, while rugged full-back Phil Bardsley may complete a free transfer to West Ham.
Gus Poyet might be able to keep some of his top stars if top tier safety can be secured this week.