Real made an attempt for Alonso last summer and are again being linked with him this week.
But Alonso said: "What I can say is that I am very calm and very happy at Chelsea, and that the club must also be with me because, although I still have two years left on the contract, it has offered me an extension.
"We are talking about it and the talks to renew are already advanced.
"If everything goes well, I think I will renew before the end of this month. In the coming days."