The 23-year old became the most expensive British goalkeeper of all time last week after the Toffees paid £25m to acquire his services from Sunderland.
"He is something special," Kirkland told Sky Sports. "I told Liverpool to sign him 18 months ago. You could have got him for a lot less then.
"He's the best I have worked with. He's a very confident lad and he doesn't have a weakness in his game.
"Normally with goalkeepers sometimes they are struggling with one aspect of the game but this lad has got the lot.
"His distribution is second to none, he makes the saves which 'keepers should make and his command of his box is the best I have ever seen."