Real president Florentino Perez could be ready to make a move for Clichy after signing Cristiano Ronaldo and Kaka in recent weeks.
Clichy told Sky Sports News: “I heard there is an interest from Real Madrid, but I have a contract with Arsenal which I intend to respect unless the club say otherwise.
“It is great to be linked with Real, but I want to win things with Arsenal.”
Atletico Madrid and Espanyol are also reported to be interested in the Arsenal defender.