Michael Essien has recommended him and told Blues boss Avram Grant to sign up his fellow midfield player before he is netted by another top European club.
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."