However, the Brazilian has since made a u-turn and insists that he wants to stay and win titles with the Rossoneri.
Allegri is assured that the player has a future at the club and played down the rift between the two of them.
"Pato wants to stay and my wish is that he does not leave," Allegri said at a news conference, "I hope and I believe that he will stay with us for this season and also for many years to come."
"There is no problem between me and Pato," Allegri continued. "The boy's outburst was because of a moment of frustration.
"You cannot always be a starter, but this is not something serious, it can happen.
"He has been training hard and he does not show any sign of being unhappy."
Pato has made only 12 appearances for AC Milan after facing niggling hamstring injuries.