The Real star continues to be linked with a move to the Saudi Pro League.
But Casillas said at a padel event: "As a Real Madrid fan, I would like Vinicius to stay at Madrid. He has had a fantastic development since he arrived.
"At first he was the subject of laughter and mockery every now and then, but he himself has become one of the best players in the world and I hope that continues like this."
On Real's season, the former goalkeeper also said: "Those of us who have played this game know that what they tell you one day has nothing to do with what they tell you another. Three months ago Madrid was horrible, Carlo Ancelotti was a disaster and now everyone says he's a phenomenon.
"This has changed a lot and you have to be prepared for March when everything is decided."