News of the World says Clichy’s agent have been contacted by the Spanish giants.
Real is keen on signing the 24-year-old next summer, following several impressive performances by Clichy.
Clichy told News of the World: “At the moment, I am focused on Arsenal and France.
“This season could be very important to me and I desire to be focused in my work. The summer of 2010 is still very far away.”