The Gunners' Champions League hopes are all but over after suffering a 5-1 defeat in the first leg of their last 16 tie on Wednesday.
Wenger reportedly has a contract offer on the table to extend his deal and when asked when a decision will be forthcoming, he replied after the Bayern match: "March, April probably".
Reports in the British media on Thursday suggested that Wenger's future will be clarified at the end of the season.
The discontent among the club's supporters has reached new heights over the past month as Arsenal have seen another Premier League title bid derailed, while a seventh consecutive exit at the last-16 stage of the Champions League looks inevitable.
But former Gunners defender Nigel Winterburn says it is unfair to pin all the blame on Wenger and urged the players to take collective responsibility.
"When you work with Arsene Wenger you will walk through situations, what you think the opposition will do, defensively how you react," he told Sky Sports.
"He will have done that [before Bayern] but when you're in real game time and things are happening very, very quickly the players on the pitch can't rely on what the manager has told them on the training pitch because certain situations may not arise.
"It's up to the players collectively to organise themselves and pull players back into midfield if they need to. Maybe push players out wider if they're being overloaded on the wide side.
"Arsene Wenger can't do that when he's on the touchline, players have to take responsibility to do it themselves."
Winterburn conceded, though, that the time has come for his ex-boss to consider his future at Emirates Stadium.
"At the end of the season, I think Arsene Wenger knows he'll have to sit down and have a real look at where he takes Arsenal Football Club or whether it's time to step aside," he added.
"We know at the moment every time they lose a game of football the swell of support against Arsene Wenger is going to grow and grow.
"He is a manager that likes his teams to go out and entertain, and I think what's lacking at the moment is that real resilience when they don't gain possession of the ball enough.
"If he was to stay as manager he would have to have a look at maybe changing some personnel and maybe looking at a different direction."