The Ivorian will take on his former manager when Galatasary face Real Madrid in the Champions League, and the 35-year-old feels that both he and Mourinho have unfinished business in west London.
Mourinho has been linked with a return to his former club in the past months, and Drogba believes the 50-year-old could help turn the club's fortunes around.
"I think for the club it is the best solution to bring Jose back," Drogba told The Guardian. "The fans want him back. He loves Chelsea.
"Because you want to rebuild a team and to give them the strength we had a few years ago, he could be the right person.
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"I don't think he has got over Chelsea and they haven't got over him. When he came he brought success; we won league titles back to back with some great football and the only thing he didn't win was the Champions League.
"Maybe that is one of the reasons why he might want to come back. It is unfinished business.
"[A return to Chelsea] would be nice, not just coaching but to help the club. For this club I gave everything and of course they gave it back to me.
"I feel at home when I go to London. When I go to Chelsea's training ground I feel like I can walk around with my eyes closed and know where I am going."