Hazard revealed in early February he had made a decision over his future, but the star attacker is yet to announce his plans.
The 28 year-old, whose contract runs until 2020, has long been linked with a move to the Santiago Bernabeu and Courtois wants Hazard to move to the LaLiga giant.
"I don't know if he is going to sign for Real Madrid, nor do I know if the club want him," the goalkeeper said. "For me, he is a great player, but I don't decide those things.
"Each one decides what he does with his life. For me, he is one of the best in the world and as a friend I would like him to be here."
Courtois played four seasons at Chelsea before making the switch to Madrid in August last year.
Hazard has scored 13 goals and provided 11 assists in 29 Premier League games this season, with Chelsea sixth on the table.