The French manager has come under scrutiny from pundits, including club hero Thierry Henry, and supporters after a period of poor results – with a run of just three wins in 12 games seeing their Premier League title challenge fall away once again.
But Merson told the Alan Brazil Sports Breakfast: “I’m bored with coming fourth every year!”
Arsenal have found themselves eight points adrift of Premier League leaders Leicester City after Saturday’s north London derby draw with second-place Tottenham.
And Merson believes Wenger’s lack of spending – they’ve signed just two players, goalkeeper Petr Cech and midfielder Mohamed Elneny, over the past two transfer windows – could cost them major silverware this season.
“This is a big club with a lot of money to spend,” the pundit said.
“If they were working on a tight budget I’d say fair enough. But to sit there at the start of the season and say we don’t need any players, and then if Leicester or Tottenham go on to win the league, I just don’t see how that washes.
“If Manchester City go on to win, you hold your hands up. They’ve got a bottomless pit of money, they can buy whoever they want…but Leicester and Tottenham can’t.
“Arsene Wenger is very stubborn. Don’t’ get we wrong, he’s a top manager, he knows his football and he’s brilliant, you don’t stay in that long if you’re not.
“But we all know Arsenal need a solid spine to the team. We all know they need a centre-half, a central midfielder player and a centre-forward. They’ve needed a top class goalkeeper for the past six or seven years, and they only got one this year!”
Asked if that means Arsenal need to let Wenger go and appoint a new manager at the end of the season, Merson added: “I think so. They have to.
“This game against Hull is very big for Arsenal, and Wenger, now.
“They haven’t got a chance against Barcelona in the Champions League, they’ve got three unbelievably hard away games in the league against Everton, West Ham and Manchester City coming up, so if they want to win the league they’re going to have to do it the hard way.
“For me, the FA Cup is the only thing they’ve got.”