The Blues defender has informed Los Blancos that he wants to join them with final details being discussed between the two parties.
Antonio Rudiger is close to joining Real Madrid after giving his word during advanced negotiations over a lucrative four-year contract.
It is unclear exactly what the 29-year-old will earn but it will be a significant pay-rise to his current Chelsea contract and similar to the £200,000-a-week offering from the west London outfit.
It is expected the Spanish giants will get their man after Carlo Ancelotti instructed his club to restart talks after failed negotiations in December.
