Reports claim the Rossoneri are keen to bring in Drogba as a replacement for Antonio Cassano.
Cassano is expected to be out of action for around six months after having undergone heart surgery earlier this week.
Cassano suffered a stroke during AC Milan’s 3-2 victory over Roma.
Drogba has long been linked with a move away from Chelsea and his contract with the Blues is set to expire at the end of the season.