The Gunners lost their FA Cup game in three years on Sunday after a surprise 2-1 defeat by Watford in the quarter-final at the Emirates Stadium.
Arsenal have lost their last three home games in all competitions for the first time since 2006 following defeats by Barcelona, Swansea City and Watford.
Wenger is coming under increasing pressure from his critics and some Arsenal supporters following their FA Cup exit and poor results in the Premier League and the Champions League.
However, former Manchester United midfielder Scholes doesn’t believe Wenger needs to win the Premier League to save his job at the north London club.
“I don’t know if he has to win the league,” Scholes told BT Sport.
“He has managed to survive the last few years without winning the league. He has done great in the cups.
“It is disappointing going out of the cup but they’ve had a great run.
“Arsenal can still win the Premier League, don’t worry about that!”
Arsenal make the trip to Champions League holders Barcelona in the second leg of their last-16 clash on Wednesday night.
Luis Enrique’s side were 2-0 winners against Arsenal thanks to Lionel Messi’s brace at The Emirates.
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