The experienced coach feels the Cote d'Ivoire star could be an invaluable asset in both Serie A and the Champions League, though he is unsure whether he would agree to a salary cut
The former Chelsea forward has been linked with a number of clubs in recent weeks, with the Rossoneri and Juventus seemingly towards the front of the queue for his signature.
Lippi, now a coach in China's Super League with Guangzhou Evergrande, feels the powerful attacker would prove a shrewd acquisition for Massimiliano Allegri, as he would compliment the creative talents of leading Serie A goalscorer Stephan El Shaarawy.
He told Gazzetta dello Sport: "Drogba is still a beast, one who makes the difference on the field. In China, he has scored eight goals in 11 games.
"If it is true that [Alexandre] Pato and Robinho are leaving, I would say he would look good in Milan. Drogba would be invaluable in both the league and the Champions League. He as the holder, [Giampaolo] Pazzini in reserve, and El Shaarawy to the left."
Lippi added, however, that the huge sum Drogba currently earns with Shanghai Shenhua means he would have to agree to a large pay cut should he opt to move to Italy.
He continued: "After winning the Champions League with Chelsea almost single-handedly, he decided to accept the economic proposal that came from China. It was a choice of football or the heart. It was a choice dictated by economic reasons.
"He probably expected something more to this new adventure from the sporting point of view, as his team only came 12th in the league. But do you think Drogba will agree to halve his salary to come and play in Italy? Well, I have my doubts."