Hazard has only featured in four games across all competitions so far this season and he is yet to send the ball into the back of the net.
"He is a world star, I know the quality he has and how he can play at the highest level," Mignolet said ahead of their Champions League meeting.
"Now he is in a new team and needs time, but I am sure he will succeed and will be a star at Real Madrid."
"[Courtois'] last weeks have been difficult after the Paris Saint-Germain game, but he has returned to his level," Mignolet added.
"He is a world class goalkeeper who always demonstrates his virtues.
"He has all the qualities to be Real Madrid's goalkeeper."