Since their FA Cup win in 2005, the Frenchman's side have fallen at the final hurdle in the Champions League final in 2006 and more recently in the 2011 Capital One Cup final against Birmingham City.
Robson feels that the problems at Arsenal are down to Wenger's management style and believes that he does not prepare his players well enough.
"I would have sacked him four years ago but I'm in the minority," the former player told talkSPORT. "Arsenal need a new manager and they need it soon."
When asked whether Arsene Wenger's status at the club makes him unsackable, Robson insisted: "In my view he's not. I wrote an article about four or five years ago when I said he was the cause of a lot of problems at Arsenal.
"He doesn't have the tactical understanding, his manner on the side of the pitch doesn't help the team, he's petulant and therefore his players become petulant. He doesn't give any information from the sidelines and his teams look under-prepared defensively.
"I wrote that article five years ago and nothing has changed my mind since. In fact, my views on Arsene Wenger are even stronger now than they were then. There's still 50 per cent of the fans which will say what a good job he is doing and we must trust in Arsene Wenger but I just don't see it.
"Arsenal still have good players," he insisted. "If somebody got hold of them and taught them how to defend, had a solid game plan and worked hard on them then I still think Arsenal can still be a very, very good side.
"For me, there's no reason why they can't promote from within. Terry Burton, who is the reserve-team boss, is an excellent coach and Steve Bould, who isn't allowed to do any work at the moment, are both candidates.
"I would like to see somebody else given a chance at Arsenal, so they can take the club forward to where it should be.
"I think there's some wonderful players already at the club and if some better signings come in I think Arsenal could be right back at the top again."