The 26-year-old has been widely linked with a move away from the north London club this summer, with the Spanish capital touted as the most likely destination.
And Casillas is certain that the Croatian would be able to bring a new level of quality to Los Blancos, and that the former Dinamo Zagreb is worthy of representing the Liga champions.
"I know him," the 31-year-old said at a press conference. "It's been some time that he's been a player at Tottenham, and he has been in the eyes of the world.
"At the last European Championship he was there. He's a very good player. I believe that he's [at Real Madrid's level].
"The boss can form this team and if he's a player that will reinforce us we're enchanted. Enchanted to have him in our group and take another step forward in this next season."
However, Casillas does not think that his side's defence needs to be bolstered amid speculation that Mourinho is in the market for a right-back.
“Wait a minute. I'm not the one you should ask that,” he pointed out. “I believe that our defence is very well covered.”