The 23-year-old has interested Arsenal this summer, just 18 months into a four-and-a-half year deal at San Siro.
However, Inzaghi - who replaced Clarence Seedorf in the Rossoneri hotseat earlier this summer - does not want to sell the Italy star and is willing to forget his troubled past.
"Balotelli is a very important player and belongs to Milan," he told the press. "I'll interact with him in the way I do with other players.
"I'll forget everything I've heard about him either in a good or a bad way because I want to get to know people to get the best out of them.
"The club make the decisions but, for me, Mario is a talented guy who plays for Milan and the national team."
Inzaghi, 40, also gave an insight into his plans for the striker this season, as he looks to get the best out of a player who struck 19 times in 43 appearances for club and country last term.
"He should be a second striker because he is the first reference point along with Pazzini," the new coach argued. "I think we'll stay that way."