Robson is in agreement with Scholes, although he believes that Wilshere's boss Wenger is responsible for the midfielder's absence of significant improvement.
"Jack Wilshere can be a world-class player. I've seen him from a young boy and he's an outstanding footballer. Paul Scholes is right though, he hasn't developed as well as everybody would have liked him to," Robson told talkSPORT. "He lacks discipline. He wants to get on the ball and charge into tackles, there seems to be no discipline.
"Who does that come from? The manager. Wenger has to make sure he has a role in the side where he knows what to do when he does, and doesn't, have the ball. He can be petulant at times. Why is he petulant? Because the manager is petulant on the sidelines and it's never been sorted out.
"If Jack gets the right manager in charge of him, and the right sort of coaching, he will become a world class player. Arsene Wenger in my view is not that manager."
Robson went on to suggest that Wilshere, who has been capped 15 times by England, may need to leave the Gunners if he is to become the player that he once promised to be.
"Like many players that have gone on to become top players, sometimes you have to move. Jack Wilshere, at some point, may have to move away from Arsenal," added the 49-year-old.
"If Arsenal change the manager and someone comes in who's really disciplined and can get the best out of Wilshere, then Arsenal will still be the right club. At the moment though, with Wenger in charge, I'm not sure Arsenal is the right club for him."
Wilshere has made 41 appearances for club and country this season, scoring five goals.