Rennes are considering trying to sign Wahbi Khazri on loan.
According to L'Equipe, the Ligue 1 side are confident that they could cover the bulk of the 26-year-old's wages.
It is not clear whether the Black Cats would be open to a temporary move. Jeremain Lens and Fabio Borini have left on season-long deals this summer, but both will make their switch permanent automatically.
Khazri signaled his intention to leave Sunderland in an interview on French TV last week, having failed to make Simon Grayson's starting line-up in any league game so far this season.
Sunderland fans booed the previously popular playmaker at Oakwell during the 3-0 defeat, though he then took to social media to state his commitment to the club.
The Black Cats would not stand in his way, seeking to move players on in order to allow Grayson to reshape his squad ahead of the transfer window closing on Thursday night.