The Ivory Coast international has been made one of Milan's top transfer targets as they look to rebuild after a dissapointing season which saw the Rossoneri miss out on qualification for the Champions League.
Drogba had admitted to being unsettled at Stamford Bridge for some time and his future has been the centre of speculation ever since Jose Mourinho left the club.
Milan vice-president Adriano Gallini revealed earlier this week that he had met for talks with Chelsea chief executive Peter Kenyon about a move for Drogba and has now told Gazzetta dello Sport that they have been given the green light to move for the striker.
"Chelsea have authorised us to open negotiations with Drogba," said Gallini.
It wasn't all good news for Gallini, though, as he revealed that Chelsea had blocked his move for Andriy Shevchenko.
"Unfortunately, the response we feared came (for Shevchenko). Chelsea consider Andriy unsellable. This epilogue makes us very sad," added Gallini.