Marin, who has signed a five-year deal with the newly-crowned Champions League winners, believes Di Matteo should be given the Chelsea job on a permanent basis.
"I hope the coach will stay because he is a great coach," said the 23-year-old German playmaker.
"I have met him a couple of times and we held positive discussions."
And on Drogba he added: "It would be great if he stayed because he is a world-class player.
"He's a big part of the team and he has done a lot for Chelsea."