Courtois was unveiled by the LaLiga giants on Thursday afternoon after completing his move from Chelsea.
Despite the transfer window being closed for the Premier League, other leagues are still allowed to buy players from England and Courtois wouldn't mind seeing his former Blues teammate in the Spanish capital.
"My goal was to come here, everyone knew it, but I could not say in the press. I am very happy and proud to be here," Courtois told reporters.
"He [Hazard] is glad that I arrived because he knew it was a dream for me.
"I would like to be always by his side. He is a great player and if he could come here it would be something fantastic."