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The Frenchman is out of contract at the end of the season and has yet to reveal whether he will extend his 21-year reign.
With the Gunners having failed to win the Premier League since 2004, there appears real appetite for change at the club and there have been a number of protests by supporters calling for Wenger to go.
But former Arsenal star Merson is convinced the 67-year-old is going nowhere.
He told talkSPORT: “I think Arsene stays, I definitely do.
“He will be there [next season], there is no doubt about that.”
Arsenal look set to miss out on Champions League football for the first time under Wenger.
It will be a big blow for the club to drop into the Europa League, but Merson believes it could boost their chances of title success in 2017/18.
He said: “I can’t see Arsene Wenger taking the Europa League seriously next season so, if he doesn’t, they are only playing once a week.
“We have seen what has happened with Chelsea playing once a week. It is a massive advantage.
“I don’t think Chelsea would have been as good if they were playing in the Champions League.”