The Italian guided Bayern to another Bundesliga title in his season in charge last term but rumours of player unrest and problems behind the scenes have derailed the German giants, who find themselves third in the league.
However, Milan are happy with Montella, despite a topsy-turvy start to 2017-18 following a major and expensive overhaul of the squad during the off-season.
"It was sad, because Ancelotti proved himself to be one of the best coaches in the world and we don't know why this decision was made," Mirabelli told Sky Sport Italia.
"We are disappointed as fans of sport, but we have a coach who is younger than Ancelotti and just as talented. We believe in this project with Montella and want to reach the end of this journey with him.
"I understand these things are very tempting for you to write about, but everyone does their own job. We say that we are holding on tight to Montella."