Annan, who plays for Norwegian side IK Start, has been one of the hottest prospects at the African Nations Cup.
German giants Dortmund have already taken note.
Essien said: "I'll do whatever I can to make Chelsea stronger. If that means when I see a good player I tell my club, I will do that."
Annan, 21, said: "It is exciting to hear of Chelsea interest in me. If Michael has recommended me, I am very grateful."