Allegri has been linked with a summer move to Roma but refuses to talk about his future until the end of the season.
But Balotelli, who was signed by the club from Manchester City in January, wants Allegri to stay.
The striker, who found the net twice in the 4-0 victory over Pescara in midweek to keep his side third in the table with two games to play, told Mediaset Premium: "When I got here Allegri was in charge and we get on really well.
"I hope he stays, as I'm really happy with him. If I were the club, I'd do everything to keep hold of him.
"I am just one of the players here and we all contribute. I was unable to get into gear today and it was a bad performance, but eventually we managed to get the points."
Allegri re-iterated he wants to finish the season before talking about his future.
"We are all focused on third place. It is not respectful to talk about my future at this time of the season.
"We'll talk about it over the summer - first with the board ... and then maybe with the journalists."