Wenger, the Gunners' boss of 20 years, is facing scrutiny after Sunday's defeat to a youthful Manchester United side, which left the north Londoners five points behind Leicester in the championship race.
The result means that Arsenal, who were top of the pile in January, have acquired just nine points from their last 21 available and Wenger's men could lose further ground if they fail to beat second-placed Tottenham at White Hart Lane on Saturday.
Merson, who played under Wenger for a season before moving to Middlesbrough, believes that unless his former side finish second behind Manchester City, the Frenchman must go.
"If Man City don't win the league and Tottenham or Leicester do then Arsene Wenger has to go," the 47-year-old told Sky Sports.
"If you're sitting there telling those fans - loyal Arsenal fans - that they don't need any new players at the start of the season and then you don't win the league in front of Leicester or Tottenham then I don't see how you can justify it.
"If Man City win the league he can turn around and say 'they've got all the money in the world and can go and buy whoever they want, so would whoever I bought have made much difference?'
"But if Leicester or Tottenham win the league after he said they didn't need any players then I don't see how he can keep his job."
Arsenal, who have not won a league title since their 2004 'Invincibles' campaign, added only Chelsea goalkeeper Petr Cech last summer, despite calls for a new centre-forward to be sought.
In January, they signed Basel midfielder Mohamed Elneny, but the Egyptian has had little impact on the Gunners' first team so far, appearing just three times in all competitions.