The Gunners now appear to be out of the title race and many fans have been calling for Wenger, who is out of contract at the end of the season, to depart after 20 years in north London.
But Manchester United legend Neville insists Arsenal should not be thinking about replacing Wenger.
Gary Neville thinks Arsenal would be foolish to replace Arsene Wenger
“Wenger's biggest challenge is that he's been there a long time and people may start to think the grass is greener,” Neville told Sky Sports.
“If Wenger was Jurgen Klopp and was currently above Manchester City, Liverpool and Manchester United – clubs that have spent £200m between them – people would say he is doing a great job.
"If you were to imagine Arsenal at the start of a season without Wenger as manager, they could end up in seventh or eighth, given the budgets they have.
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Arsenal fans have been calling for Arsene Wenger to leave the club
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“If Wenger were Klopp now, we'd be saying he is doing a good job because he's 18 months in. Actually, isn't Wenger not doing a great job full stop?
"It was embarrassing seeing Arsenal fans slating Wenger after the Chelsea game and he doesn't deserve that. He has done an unbelievable job.
“If he were to announce his retirement, everybody would plough in with tributes and in 10 months' time, they might be thinking, 'I wish he was still here'.
"There isn't a part of me that wants Arsenal to replace Wenger when the club have supported him for so many years. I feel very uncomfortable suggesting the grass may be greener and that he should move on."