Milan are looking for a new striker after Antonio Cassano was ruled out for the season following heart surgery and Ancelotti, who enjoyed success as manager of both Chelsea and the Rossoneri, urged the Serie A club to sign the duo.
"Certainly they are great players, in good physical condition," Ancelotti said. "They are players of great quality and attitude. I see both fitting in very well at Milan but that does not mean one of the two are going to go."
Galliani has also spoken in glowing terms of Drogba and Anelka, but played down talk of January bids for the Chelsea strikers.
"Ancelotti understands football," Galliani told Gazzetta dello Sport. "Perhaps we will take them both!
"Seriously, it is not certain that we will sign anyone in January. If we did it would be a loan because I promised to keep a place for Cassano.
"Anelka is a major player but I have been in love with Drogba since he played in Marseille."
Drogba, who has been at Chelsea for seven years after a £24 million move from Marseille, and Anelka, who signed for £15 million from Bolton in 2008, are out of contract at the end of the season.