Ancelotti lost his job following Wednesday’s embarrasing 3-0 Champions League defeat to Paris Saint-Germain.
The Italian led Bayern to last season’s Bundesliga title but they are currently third in the league.
Ancelotti won the Serie A, Champions League, Coppa Italia, Supercoppa Italiana, UEFA Super Cup and Club World Cup titles for the Italians. He was in charge of the team between 2001 and 2009.
“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.”
Milan were shocked by Sampdoria in the Serie A last week and were lucky to scrap through in a narrow 3-2 win against Rijeka in the Europa League on Thursday, having surrendered a two-goal lead.
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