No team in Champions League history has overturned a two-goal first-leg home deficit, and the difficulty is heightened by Jack Wilshere and Lukas Podolski's absence through injury
They trail 3-1 from the first leg at the Emirates Stadium last month, when goals from Toni Kroos, Thomas Muller and Mario Mandzukic gave the German giants a comprehensive away victory.
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It sounds like a mountain to climb because it is. Only two teams have ever advanced after losing the home leg of a Champions League knockout tie – Ajax against Panathinaikos in 1996 and Inter against Bayern in 2011 – and neither overcame a two-goal deficit to do so.
Recent history is no kinder. Bayern have not conceded three goals in a game since the German cup final against Borussia Dortmund, some 10 months ago. They also scored twice that day. In 2013, they have only conceded four goals in 10 matches in all competitions.
Still optimistic? Well, Arsenal will also have to do without talisman Jack Wilshere – who Goal.com exclusively revealed has inflamed the same ankle which contributed to his 16-month lay-off last season - and first-leg scorer Podolski, both ruled out with injuries.
First-choice goalkeeper Wojciech Szczesny will also not feature, having been "affected" mentally by the number of games he has played, according to Wenger.
But Bayern also have absentees. Winger Franck Ribery is missing with an ankle problem, while Bastian Schweinsteiger and Jerome Boateng are suspended.
And Wenger himself, ever the optimist, has not given up hope of making the impossible possible.
"I am convinced that if this team can find a big game, with a big win, you will see a completely different animal," he told reporters.
"We have another opportunity tomorrow night and I hope the team take this chance.”
In such a situation Arsenal’s best hope might be a complacent Bayern, but Muller insists this will not happen. "I don't have any worries we might take the match too lightly," he insisted. "We will step on the gas. Even if something goes wrong in the match, we should be able to pick ourselves up."
We are in miracle territory, then. But then, aren’t miracles what the Champions League is all about?