Wenger raised eyebrows on Friday when he said he was not "untouchable". But Van Persie disagrees.
"I don't think he is ever under pressure at Arsenal because he has done really big things for the club," he said.
"I think the boss has trust from the people above him. When you sign for Arsenal, you know you are going to have the same manager for some years."
Van Persie has only played 20 games this season and admits that the midweek defeat by Liverpool was typical of a disappointing season.
"I started out with fantastic ambitions but ended up with a knee problem. It has been very frustrating."