Seb Larsson has offers from clubs all over the world, his agent has told Swedish media.
The 31-year-old sees his Black Cats deal expire in the coming weeks, having played over 200 games in all competitions over six years on Wearside.
It is not yet clear whether Sunderland will attempt to persuade him to stay, with the club's retained list yet to be released.
David Moyes had said before his resignation that he would look to keep on one or two players 'who know the club', with a high squad turnover expected before the Championship campaign begins. That suggested that the likes of Larsson and John O'Shea may be offered new deals. There has been little movement since then with the club searching for a new manager.
Larsson's agent has said that the midfielder is keen to stay in the UK, categorically ruling out a move back to his native Sweden.
He told Fotbolldirekt that 'there also clubs in China and Turkey' who have submitted bids, but that he is keen to extend his 16 year stay in the UK.
Larsson is one of a number of players soon to be out of contract, including Steven Pienaar, Joleon Lescott, Victor Anichebe and Jan Kirchhoff.
So far George Honeyman is the only player to commit to a new deal, extending his time at the Stadium of Light for two years.