The Championship side want to appoint a new manager after they parted ways with Tony Mowbray.
Caretaker Mike Dodds is currently managing the first team and has won both of his games keeping the hot seat warm.
Sunderland are seriously considering bringing in Reims boss Still, who is also claimed to be keen on a switch to the north east.
It has also been suggested that the Black Cats chairman Kyril Louis-Dreyfus has already held a conversation with Still to tempt him to take the Sunderland job.
However, even if Sunderland do offer the job to Still, it is by no means certain they will be able to appoint him.
According to French outlet Maxifoot, Reims have not made any plans to let Still go mid-season; he is under contract until 2025.
As such, Reims may not agree to a compensation offer from Sunderland for Still and could dig their heels in.
Still is unhappy at the club’s plans for the January transfer window given he is set to lose players to the Africa Cup of Nations and Asian Cup.
