Brady, who heads the Arsenal Academy, says Wilshere will soon be a regular in the Gunners first team and with improvement will become a fantastic player.
"He is a special kid. He has got great awareness with his passing ability and he can run with the ball," Brady told Setanta Sports 1.
"He just needs to keep on learning but he is the kind of kid who'll want to learn and do better.
"I think he has a tremendous career in football ahead of him."