The Rossoneri are supposedly keen to lure the veteran attacker to San Siro this winter, and the 45-year-old would happily welcome the striker
The Cote d'Ivoire international is continually being linked with a move away from Shanghai Shenhua, and Milan is believed to be one of the teams interested in signing the former Chelsea star.
"I would obviously be satisfied if Drogba were to join Milan, just as I would be happy if any other champions would sign for Milan. The bigger the player, the better for the team," Allegri told Sky Sport 24.
He added, "There is not much to discuss when it comes to great champions, especially when an individual would add something to the entire club.
"This is a decision the club has to make, though. The current strategy is working fine. We have to take the economical situation in Italy into account when we do something."
Drogba is currently active at the Africa Cup of Nations as Cote d'Ivoire aims to win its first major piece of silverware since winning the competition in 1992.