The Cote d'Ivoire star played under Mourinho when he was in charge of the Blues between 2004 and 2007, and he believes they are similarities between him and current boss Terim.
"I have a lot of memories of him [Mourinho]," Drogba told the club's official magazine. "He's always in the spotlight, and he looks out for everyone. He tries to get the best out of every individual. Fatih Terim is like Mourinho in that respect. He's close to the players."
Drogba then reflected on his Champions League debut against Madrid in 2003, where he scored a goal for his former side Olympique Marseille in their 4-2 loss at the Santiago Bernabeu.
"The Bernabeu game will be very special for me. I played my first Champions League match there against the Madrid 'Galacticos'," Drogba said. "I scored my first goal, even though we lost 4-2 – it was in the group stages of the 2003-2004 campaign with Marseille. I'll never forget that day. It was very important for my career."