But while Casemiro feels Neymar would enjoy a good friendship with Madrid star Ronaldo, he believes his international team-mate will stay at PSG.
"[Neymar] has always been spectacular, since he was 11 years old. He does crazy things," he told El Partidazo .
"I don't think there is any chance that he will come to Real, but you have to ask [Madrid president] Florentino Perez.
"He knows that the door is always open for him in Madrid, but he is happy in Paris. He always says that he is happy there, that he is comfortable in Paris. There are many Brazilians there too, it is very quiet there, but whether it's possible you have to ask Florentino.
"With the quality that he has, I would sign him for sure. I hope he comes this season.
"He is a great player, one of the top three in the world. He can do whatever he wants off the pitch if he continues to do what he does on it.
"He would get along very well with Cristiano, very well."
A switch to Madrid would likely see Neymar play with Ronaldo, having spent four seasons alongside Lionel Messi at Barcelona.
Casemiro has no doubt about who is the world's best, unsurprisingly backing his Madrid team-mate.
"Messi is a great player, but I'm staying with Cristiano," he said.
"For me, Cristiano is the best player in the world."