Wigan have announced Uwe Rosler as their new manager after agreeing compensation with Brentford.
Marseille have parted company with manager Elie Baup in the wake of Friday's defeat to Nantes at the Stade Velodrome.
The striker has been linked in the Italian media with a possible move abroad after being constantly in the spotlight for his actions on and off the pitch.
The 23-year-old Italy international joined AC Milan from Manchester City in January and is contracted to the Rossoneri through to June 2017.
"He will not leave in January," Allegri said on www.acmilan.com. "Absolutely not.
"I think Mario should be left in peace. It's not difficult to manage him.
"There's far too much discussion of the man's private life. I think that Balotelli should be judged for what he does on the pitch like all other players."
Allegri claims it would be wrong to read too much into his decision to substitute Balotelli in Sunday's 3-2 defeat at Parma.
"It happens that players play badly but if you are Mario then everything is blown out of proportion," Allegri said. "Mario didn't play well against Parma but I'm sure he will make amends against Lazio.
"He scored 12 goals in 13 games last year.
"In the first half of the season he has done great things."
Balotelli, who has scored three goals in five league appearances for the Rossoneri this season, is expected to lead Milan's attack in Wednesday's match against Lazio.