The Argentine moved to the Rossoneri in January on loan, but the Diavolo have decided against paying the 8m fee agreed at the start of the year to keep him at San Siro.
"Maxi did well for Milan when he was called upon," agent Andrea D'Amico told TMW on Wednesday. "He also became a fan favourite.
"He has behaved in an excellent manner, putting himself under the spotlight. He is a top level player and now we'll have to work to find a solution for him."