Carvalho left the Bernebeu in June to join Monaco, and he believes that his compatriot also wants to move away from Madrid.
"I think that he wants to move on because he thinks that it would be the best thing for him to do career-wise," the 35-year-old told A Bola.
"Personally, I think he should continue because he meets Madrid's requirements. He played well in practically every game last season.
"He's a great left-back, to the point where he even made a few of his critics change their opinion about him. I do think that he has a place at Real Madrid."
Manchester United are thought to be in the market for a new left-back, with a bid already thought to have been submitted for Leighton Baines.
Coentrao might be a cheaper option, with Everton unlikely to settle for much less than £20million for their defender.