Didier Drogba is currently engaged in a protracted farewell/my ankle hurts/where the heck is Loïc Rémy tour, but what happens at the end of the season when his one-year deal expires? Nothing, which is to say that he's staying right where he is. Although he won't be playing:

It is a return to stay. No longer will there be more (Drogba) in China or Drogba playing at Galatasaray. Drogba will be a coach or assistant youth football team or the main ambassador of Chelsea or assistant director of sports. There will be a role for him what he wants. He is a player who Mr. Abramovich wants at the club. Source: Telegraph.

Personally I think this is great. While I don't think Drogba is what we need as a footballer right now his stature at the club is unquestioned and he'll be a phenomenal mentor for everyone, not just the younger players. And I also like having him around in general, because Didier Drogba is great and I heart him. No surprise that Roman feels the same way.