Drogba and Mourinho enjoyed a successful three-year relationship during the Special One's previous stint at Stamford Bridge.
The Blues won two Premier League titles, two League Cups, an FA Cup and a Community Shield during that period, before Mourinho was sacked in September 2007.
"He can return the glory days," Drogba told the Daily Star.
Drogba has been linked with a return to England this summer and the 35-year-old appears to be keen on such a move.
Drogba's current contract with Gala is due to expire in June 2014.