The 33 year-old has a year left on his current Blues contract and is weighing up his future at the Bridge.
Corriere dello Sport says Milan see Drogba as an ideal partner for star striker Zlatan Ibrahimovic. However, they will face competition from Inter.
Samuel Eto'o has made a personal request to Inter president Massimo Moratti to sign the Ivorian.
In both clubs' favour is Drogba's love for the city. The striker is a regular visitor to Milan.