Drogba could return to Europe during the current transfer window, just six months after he left Chelsea to join Shanghai Shenhua on a lucrative deal.
The 34-year-old has reportedly failed to settle in China and agent, Carlos Arino Bajo, revealed he has an option to end his two-and-a-half year contract early.
"Didier has a termination agreement with the Chinese club and I think he has a lot of possibilities to move to Italy in January," he told tuttomercatoweb.com.
"There is real interest from Juventus and AC Milan, and it is the same from Didier regarding the transfer.
"There have been contacts with both clubs and next week we will hear from them again. He would love to compete in one of the world's best leagues, such as the Italian Serie A."
The link to Juventus is, however, at odds to comments made by boss Antonio Conte last month.
Conte ruled out an approach for Drogba, who scored the winning penalty in Chelsea's Champions League final success in May, despite reports the Serie A leaders were keen to sort out a deal.
Drogba would be unavailable to play for any new club until after the African Nations Cup, with the final due to be played in Johannesburg on February 10.
The Ivory Coast striker has been training with Chelsea in the lead-up to the tournament after returning to Europe following the end of the Chinese season in early November.