The Portuguese feels his fellow countryman is indispensable to the club and is desperate for him to extend his stay in the Spanish capital.
The Portugal international's current deal with los Blancos is due to expire in the summer of 2015 and reports suggested he was ready to leave the club after claiming he was unhappy in the capital earlier this season.
However, club president Florentino Perez insisted on Tuesday that Madrid will renew the 28-year-old's contract shortly, much to the satisfaction of Mourinho.
"It's clear that he's the kind of player who could play anywhere he wants," Mourinho told TVI. "It would be great for Madrid and for himself if he signed a contract extension here. He's a fantastic player and indispensable for Madrid.
"When you have a player of his caliber, you must do everything within your power to hold on to him."
Ronaldo has been heavily linked with Paris Saint-Germain, but the Ligue 1 leader recently stressed that the club has yet to make an offer for the player.