However, the Belgium goalkeeper is confident he'll be friends with the Costa Rican.
He said, "When I came to Chelsea I did it to replace (Petr) Cech, I still talk to him today, the goalkeepers are part of a dressing room and they are also friends, I will do everything so that there is a good feeling within the group.
"I will help Madrid win matches and trophies."
On Real legend Iker Casillas, Courtois feels he has the same mental strength.
He added: "When I saw him play, what struck me the most is that a goalkeeper at 18 years old, with that pressure, performs like that, you have to be mentally strong, I made my debut with Genk at 16, at Atlético with 19 ... I think that's very important, and his ability between sticks was impressive."