Leonardo could reunite with old Milan companion Carlo Ancelotti at Paris Saint-Germain.
The two worked well together as transfer scout and Coach at San Siro, winning the Champions League.
Leo is now the director general at PSG, having already brought in Serie A players like Jeremy Menez, Salvatore Sirigu, Momo Sissoko and Javier Pastore.
According to L'Equipe, Coach Antoine Kombouaré is already under pressure after losing the first game of the Ligue 1 season against Lorient.
The prime candidate to take over is Ancelotti, who is a free agent after he was sacked by Chelsea.
Ancelotti has won the League title in both Italy and England, so could turn his focus to France.