The Blues have confirmed the long-serving assistant wants to quit to join West Ham but they are refusing to let him go.
Clarke is desperate to link up with former team-mate Gianfranco Zola, who has taken over at the Hammers.
A Blues statement read: "Chelsea can confirm that West Ham have made an approach with regards to talking to Steve Clarke. They have not been given permission to talk to him.
"Steve Clarke has tendered his resignation as assistant first team coach. We have not accepted his resignation. Talks are continuing."
The Scot has spent over 20 years at Stamford Bridge as a player and coach but he is now ready for a new challenge.
After working with Ruud Gullit at Newcastle, Clarke was assistant to Chelsea managers Jose Mourinho, Avram Grant and Phil Scolari.
Big Phil said: "I have been told he is going I am sad but I understand Steve. All people have projects in their life.
I dont agree with his decision but I am happy for him because I like Stevie.
I like him as a person and as a coach and I wish him all the best.
Yesterday I invited Steve to visit my house and we discussed the situation between West Ham and Chelsea.
I told him what I thought and this morning told Peter Kenyon what I think about Steve, that he is very important for me and for Chelsea.
He is a man that is a link between me and the players and between me and the staff. He knows Chelsea very well and English players and clubs.
When he told me about his projects I said to him I could be the man who would open more chances for him to be the head coach in England or in other countries.
And I said I would give him more responsibility at Chelsea and would tell the press that Steve wanted to fly alone in the future.
I dont know what happened in the night but when I came here in the morning I heard he had resigned.