Carvajal said he would welcome the Brazil international to the Santiago Bernabeu if Madrid president Florentino Perez was eager to sign the star forward.
"If he was born to play in Madrid, I don't know," he told Cadena SER.
"Madrid always want the best in the world. If the president is determined to sign him, we will have to save a locker."
Madrid are also linked with a move for Alvaro Odriozola, the Real Sociedad right-back who would likely put pressure on Carvajal for his spot.
But Carvajal said he would be happy to see his Spain team-mate join him at Madrid.
"If the coach [Julen Lopetegui] and the president believe it necessary, welcome," he said.
"I think he is a great player, young, with good defensive skills. He's a very complete player."