Drogba told The Sun: "Jose needs to come back. He is a winner, he is close to the players. He went to Inter and is now at Real Madrid but he is still talking about Chelsea so he loves this club.
"The fans want him back. I think for the club it is the best solution to bring Jose back because you want to rebuild a team and to give them the strength we had before. If he is thinking about bringing him back he has his reasons. I don't think he has got over Chelsea and they haven't got over him.
"When he came he brought success 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."
Chelsea have had seven managers in the past five-and-a-half years since Mourinho's departure from the club.