Wenger is once again under pressure with Arsenal languishing in sixth in the Premier League table.
The Gunners missed out on Champions League qualification for the first time this century last season and look likely to suffer the same fate this term.
Arsene Wenger was quizzed over his future at his press conference yesterday and once again reiterated his commitment to the club, claiming he had turn down many offers to stay at Arsenal over the years.
But Robson did not like the way the Frenchman said it.
“Did you see his interview yesterday?,” he said on talkSPORT.
“‘I’ve turned down the world to stay at Arsenal’ – he’s so arrogant, it’s untrue.
“The reason he stays at Arsenal is he can do what he wants, he’s not under pressure and he gets paid nearly £10million a year.
“That’s why he stays at Arsenal, not because he’s loyal to the club.
“If he was loyal to Arsenal and loved Arsenal so much, he would have left two or three years ago.”
Arsenal are in Premier League action this evening against Manchester City at the Emirates (7.45pm).
The Gunners lost 3-0 to Pep Guardiola’s side just four days ago in the Carabao Cup final.