Bonucci, 31, only joined Rossoneri from the Old Lady last year in a €42m (R660m) transfer that was intended to spark the renaissance of the fallen Italian giants.
However, with the recent turmoil surrounding the ownership of Milan and their failure to qualify for the UEFA Champions League after significant investment - the club captain is seeking a swift exit.
Speaking at a Press conference on his side's pre-season tour of the United States, Gattuso admitted Bonucci's future is out of his hands.
"I've spoken to Leo and you need to be honest and say things as they are," he said.
"Leo had a meeting with me, but I am not the club and he needs to talk to the directors.
"Until he leaves my dressing room, I want to see the Bonucci I've seen over the last 12 days – a professional Bonucci, he is the first to push the group and he is behaving as a great captain.
"Then it will be up to Leo and the club to decide, but I hope that Bonucci can stay here. He is a player with mentality and talent.
"I think that when a player expresses a desire, the Coach must do all he can to convince him to stay."