Courtois is in his third season with Real.
"I'd love to stay many more years here," Courtois told El Larguero.
"It would be great to spend the rest of my career here."
He continued: "I'm doing well now.
"After the Levante game I felt something in my groin, but it was only a small thing.
"I probably could've played with Belgium if we had had a super important match, but it was better to rest given the amount of matches we've got coming up. I've been resting for a few days now and sometimes that's the best thing to do for your body."