The ex-Chelsea striker, 34, is ready to terminate his contract with Chinese side Shanghai Shenhua after just seven months and to return to Europe to a big club.

Juventus have also expressed their interest in Drogba who is reportedly asking for 10million euros in wages for an 18-month contract in Italy.

Milan, meanwhile, have dropped the Kaka deal and Manchester City’s Mario Balotelli is too expensive for them at 28million euros (£23.5million).

Allegri told Sky Italia: “Champions of his (Drogba) calibre are very welcome. (Vice-president Adriano) Galliani will know if the deal is feasible.

“I’m calm, the club is just thinking about what could help us out and what we could do about it.

“A player like Drogba would certainly improve both the technical level and self-esteem of the team. We’ll see what the club are able to do, otherwise we’ll carry on as we are, looking to have a good second half of the season because that is our objective.

“It will be difficult, though, because we still have to face some teams with a high level of technical quality.”

Milan is now in sixth place in the Serie A table with Sunday’s victory over Bologna and potentially a candidate for europe.