The Gunners suffered their second Premier League defeat from three matches this season when they were beaten 4-0 at Liverpool on Sunday.
Former Arsenal striker Thierry Henry described the performance as “unwatchable” while Gary Neville was scathing in his assessment.
Ex-England defender Mills told The Debate on Sky Sports Premier League that Wenger, who joined the club in 1996, is putting his entire legacy in danger this season.
“It’s like that boxer having one too many fights and it going wrong,” he said. “If this is a really bad season, and they finish seventh or eighth, and don’t win anything, then that’s what Arsene will be remembered for.
“My worry would be that it destroys his legacy and everything he has achieved. It will be soured and his legacy will be tarnished.”
Mills added: “There is no fear in playing against Arsenal anymore and that’s a massive change. I almost think it’s an arrogance in Arsene Wenger or the players thinking they are too good.
“West Brom or Huddersfield can be organised and make themselves difficult to beat and they are, without being disrespectful, nowhere near as good technically as Arsenal. Is Arsene Wenger not prepared to tell his players to do that or are the players not prepared to do that themselves?”
Wenger, who signed a new two-year deal at the end of last season, has come in for criticism for his team selection against Liverpool.
Neville does not think the manager is the only person to blame for Arsenal’s struggles, but says these are worrying times for the Gunners.
“I don’t think the finger should be pointed solely at Arsene Wenger,” he said. “The foundations are totally wrong and are crumbling. When they lost 8-2 to Manchester United [in 2011] it didn’t feel as bad as this.
“Now it seems like a crisis, a moment in the club’s history when you think something has to change, whether that’s the manager, the board, the players…There have to be big changes.”
Former Arsenal forward Alan Smith said he thinks there should be a change of manager, but doesn’t see it happening.
“The longer they are out of the top four, Arsenal can sink,” he said. “They have to be very careful how they handle things. I thought the natural moment was the end of last season and that would have been good for all parties, but the logical and sensible thing would be to have a change of manager and different methods.
“It’s a plumb job, so many would scramble over hot coals to get the job. But I don’t think Arsene would ever contemplate walking away, it’s his life, he’s married to the job, but sometimes you have to ask yourself am I doing the right thing for Arsenal.”
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