The teenager is aware Real are planning a bid for his services and told his personal website: "I've wanted to go to such a club."
Altidore's agent, Richard Motzkin, told AS: "For Jozy, that Real Madrid wants to sign him is a genuine honor.
"Jozy is very happy because Real Madrid shows interest in him. We know about the reports coming from Spain. We will see what happens, but he is very excited. It is logical."