The Portugal international, 28, has already made over 500 official appearances at club level, but still has a long way to go if he is to catch up with Giggs, who recently played his 1000th game.
"I am sure Cris can do it but I don’t know yet if he wants to," Mourinho was quoted as saying by The Sun. "That is the point with Giggs and Scholes. They still can play and they still want to play. I just hope for the good of football that Cris will want to as well."
Mourinho also had his say on Madrid's chances in the Champions League, and refused to get carried away after the Blancos' win over Manchester United.
"Winning at Old Trafford was, of course, an important win and I know we can go on from here to win the Champions League," he said. "But I also know we can be out in the next round because the Champions League is full of good teams. So I am calm and I am cool."
The draw for the quarterfinals of the Champions League takes place on Friday in Nyon.