The Portuguese is confident his now former team-mate will remain at the Santiago Bernabeu, while revealing his disappointment at how his time at the club came to an end
The defender joined the free-spending Ligue 1 new-boys at the end of May on the back of three years at the Santiago Bernabeu.
And though his time at the club didn't end on a positive note, with the club dethroned as Liga champions by Barcelona and suffering Copa del Rey final defeat to Atletico Madrid, the Portuguese is confident Madrid will soon be boosted by Cristiano Ronaldo signing a new deal at the club.
He told Marca: "The president is doing everything he can for Cristiano to sign a new contract and he'll stay."
Los Blancos were dogged by publicised spats, notably between coach Jose Mourinho and key players like Iker Casillas and Pepe, for much of last season.
And the veteran stopper believes the underlying disagreements that marred their campaign could have been managed better.
"We felt that we didn't end the season well. When we should have been stronger, we weren't," the 35-year-old added.
"I don't know whether or not Pepe feels he made a mistake [publicly criticising Mourinho], or whether he is sorry, but it's something that could have been avoided by talking face-to-face.
"If you aren't winning, you have to stick together, be even stronger. But this year, as a dressing room, we should have been more united during the tough times."
Despite the debacle, Carvalho still looks back on his spell in the capital with pleasure, claiming he had achieved a lifelong ambition by playing for the club.
"I was very happy at Real. It was something I'd always wanted and I fulfilled a dream," he continued. "These past two years with my injuries, I was sad at not being able to play. I was always fit at Chelsea.
"I was on cloud nine during my first season at Real Madrid. That year gave me everything. It might have been the best time of my career.
"Before joining Chelsea, [president] Florentino [Perez] spoke with Pinto da Costa [Porto chairman] and [Luis] Figo called me. I was eager to sign, but the offer was low back then.