In the third book, he basically outright says he's Jesus.

When Edmund and Lucy are told they won't be returning to Narnia, Edmund asks if Aslan is also in the human world.

“Are you there too, Sir?” Edmund asks. “I am,” said Aslan. “But there I have another name. You must learn to know me by that name. This was the very reason why you were brought to Narnia, that by knowing me here for a little, you may know me better there.”