Many will remember Rodgers from his mostly impressive spell at Liverpool, where he came within touching distance of winning the Premier League.
He has enjoyed success in Scotland, and it will be interesting to see whether he is tempted by a return to the Premier League.
The Sun claims that Southampton's owner Gao Jisheng wants Rodgers on the advice of Les Reed, the club's vice-chairman.
But it is unclear if Rodgers has any interest, given his comfortable position at Celtic. He would be giving it up for a club that may get relegated this season.