The former Chelsea striker is being heavily linked with a return to Europe following just seven months in China after reportedly struggling to settle at his new club.
Serie A giants Juve and Milan are believed to be keen on bringing the UEFA Champions League-winning striker to Italy.
Rossoneri chief Massimiliano Allegri spoke of his admiration for the frontman earlier on Wednesday, saying he would be "very welcome" at the San Siro.
Drogba penned a two-and-a-half-year deal in Shanghai when he joined in a lucrative move in the summer after his Chelsea contract expired.
Reports suggest the 34-year-old, currently representing Ivory Coast at the Africa Cup of Nations, could terminate his contract early.