Casillas, 29, shares England coach Fabio Capello's view that Hart can become the world's No.1 keeper.
He told the Daily Star Sunday: "I totally agree with Capello that Joe Hart can be up there with the best in the world.
"If I am being honest, over the last five years I don't think there has been a keeper close to Gigi Buffon, or myself. But from what I have seen of Joe Hart, he really can be great.
"When Buffon and I are well into our thirties, Joe will be at his peak. And I expect him to be the No.1 keeper in the world. Everything he does is so natural and he has that goalkeeper's instinct, which you can't just learn.
"Apart from a handful of games with England, he hasn't played at the top level yet and, when he does, he will get even better."