The Sun says Italian giants' technical director Ariedo Braida met Drogba's representatives in Milan on Wednesday, a day after their Champions League defeat to Arsenal.
A source close to the Ivory Coast striker said: "Milan are crazy about Didier. There was a meeting in Milan this week and the Italians said Didier is their priority for this summer."
Milan's message to Drogba, 30, was that he has to put pressure on Chelsea to lower their asking price.