The former Chelsea man has endured a nightmarish two years in the Spanish capital, with a spate of injuries restricting him to just 43 appearances and five goals for the club.
Hazard has been tipped to reunite with Chelsea and end his torrid stint at the Bernabeu, but Courtois does not expect his compatriot to call time on his Blancos career this summer.
Speaking to Le Soir, Courtois said: "I'm 100% sure he's staying. He doesn't want to move. Only the Madrid press writes about the desire to leave.
"He wants to continue, play free of injuries and win titles. At Real Madrid there is criticism all the time and for everyone. Gareth Bale was criticised, but he won the Champions League and scored a double in the final in Kiev.
"We all know that in Madrid there is pressure and criticism from the press and the fans. But Eden can handle that. I know him well enough to say it. He can still change everything. He still wants to be an important player for Madrid and win titles."