The experienced attacker has reportedly attracted the interest of the Serie A champions and could be on the move to San Siro this summer
The San Siro side are keen to take some weight off the shoulders of Zlatan Ibrahimovic as their main attacking focus in the Champions League next season and head coach Massimiliano Allegri considers Drogba to be the perfect addition.
The 33-year-old struggled to find his best form in the 2010-11 campaign and could find regular first team football at Chelsea hard to come by next term following last winter's arrival of Fernando Torres and the expected transfer of Anderlecht wonderkid Romelu Lukaku this summer.
Therefore, the veteran attacker could be on the move and Milan are eager to add Drogba to their front line.
The striker's current contract runs until 2012, but Chelsea appear to be ready to cash in on Drogba if the price is right.