Ancelotti was fired by Bayern on Thursday after a disappointing run of results that culminated in a 3-0 UEFA Champions League thrashing against Paris Saint-Germain.
That left Bayern behind their French rivals in Group B, and in the Bundesliga the reigning champions trail Borussia Dortmund by three points after six games.
A league defeat to Hoffenheim and recent draw with Wolfsburg have left them off the pace, and ultimately cost Ancelotti his job – although there were also reports of disharmony in the dressing room.
Ahead of Milan's Europa League win over Rijeka, club director Massimiliano Mirabelli dismissed talk of Ancelotti returning to San Siro, but Montella would gladly have him board.
"I hold him in great esteem," said the Milan boss.
"I went to follow his training sessions when I started this job and have always thought of him as a brother.
"If he wants to come here, he can be my assistant or maybe I can be his!"