At 39, Ramos has played 26 games and scored seven goals, quickly becoming a leader on and off the pitch.
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Talks over a new 12 month deal are expected to kickoff in the coming weeks.
He told El Chiringuito: "I'm very happy, I can't complain. I'm happy, Mexico has welcomed me in an extraordinary way. The club has an interesting project and we hope this season goes well.
"My contract expires in December, but I'd like to stay: we feel comfortable here and very happy."
On the weekend El Clasico, Ramos added: "You know I'm a Madridista to the core. I hope Madrid wins and that my friend Kiki (Mbappé) has a great game.
"I speak to him often, he's playing at a very high level, and I hope the three points stay with us."