The Gunners boss announced that he will leave the north London side at the end of the 2017-18 Premier League season.
Arsenal are in sixth spot in the Premier League table and long way behind Tottenham Hotspur in the final Champions League spot.
Wenger’s side lost 3-0 to Manchester City in the League Cup to miss out on some domestic silverware this term.
Arsenal can still qualify for next season’s Champions League if the Gunners manage to win the Europa League in the current campaign.
The Gunners haven’t won the Premier League title since 2003-04 and Arsenal appear to be regressing under the Frenchman.
Arsenal finished in fifth place in the top-flight table last term after the Gunners finished behind Liverpool FC in the race for a Champions League spot.
Former Manchester United defender Neville believes Arsenal need to make a swift appointment to stabilise the club after Wenger’s announcement.
“There is no excuse now for Arsenal not to have a new manager in place by the end of next week, to rid speculation of who it could be, to make sure the new manager can be across the current squad, the current data, the current plans, the spending for the summer, all of the things that take so much time, particularly with a World Cup with players going off and agents getting distracted,” Neville told Sky Sports.
“Arsenal have to act now, and I’m sure the decision this week was to give Wenger the right send-off, but also to allow Arsenal to put the plans in place to ensure the transition is smoother than it would be at the end of the season.”
Arsenal signed Borussia Dortmund striker Pierre-Emerick Aubameyang and Manchester United midfielder Henrikh Mkhitaryan in the January transfer window.
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