Cattermole has spent the last nine years at the Stadium of Light, with the 30-year-old making a total of 227 appearances in all competitions.
However, Sunderland are said to be open to offers for the defensive-minded midfielder after relegation to League One, and it appears that one of Cattermole's former managers is eyeing up a move.
According to TEAM Talk, Bordeaux boss Gus Poyet is assessing the English market for potential bargains and that has resulted in interest in Cattermole.
Poyet was manager of the Black Cats between October 2013 and March 2015, while the Uruguayan had earlier enjoyed a successful period with Brighton & Hove Albion.
Cattermole still has three years remaining on his contract, but Sunderland are unlikely to demand big money.