"Champions of his quality are very welcome," Allegri told Sky of the 34-year-old, currently with Ivory Coast at the Africa Cup of Nations and keen to leave Shanghai Shenhua only months after joining from Chelsea following their Champions League triumph.
"[Chief Executive Adriano] Galliani knows if we are talking about a doable deal. Certainly Drogba would increase the technical level and belief of the squad."
Milan, only sixth in Serie A but in the Champions League last 16 where they face Barcelona, have also been linked in the media with Manchester City striker Mario Balotelli despite club owner Silvio Berlusconi questioning his combustible personality.
Milan's pursuit of Drogba means Serie A leaders Juventus are likely to go for other striker targets including Olympique Lyon's Lisandro Lopez. Athletic Bilbao's Fernando Llorente is poised to join Juve in July.
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