The 67-year-old has never failed to guide the Gunners into a qualification spot for the competition in his 20 full seasons at Arsenal, but his side face an uphill battle to finish in the top four this season.
A win for Wenger's side would lift them to 75 points – four more than they managed last term, when they finished second – but that would not be enough to move into the top four if Liverpool beat Middlesbrough and City avoid defeat at Watford.
But Wenger, pointing to City's dramatic title win in 2011-12 when Sergio Aguero struck the crucial goal in injury time, insists anything is possible.
"We can do 75 points, so let's do it," said the Gunners manager. "Will it be enough or not? I don't know. If you had to bet, you would say: 'No, it will not be enough'. But you never know.
"Man City won the championship in the last minute against QPR, so it can happen.
"It's unpredictable. Liverpool will certainly be up for it; Middlesbrough will be up for it. Is Liverpool favourite? Yes. But we played 0-0 at home against Middlesbrough. It was not easy."
Arsenal were in a similar position in 2005-06, when they leapfrogged Tottenham to go fourth on the final day of the season after their north London rivals – whose squad had been blighted by food poisoning the day before – lost 2-1 to West Ham.
But Wenger says the fear of missing out that year was not as great given that they had the chance to qualify for the following season by beating Barcelona in the final, although they went on to lose that match 2-1.
"In 2006, we had the Champions League final to prepare and this season we have the FA Cup final," he said. "We thought we had the chance to win the Champions League and to be in the Champions League again, so the fear to be in it was less big.
"This time, we are less likely to be in it but we still can manage it by only focusing on what we think is important, which is to win against Everton."
Wenger has also hit out at the importance being placed on a top-four finish following years of criticism for delivering few other successes of note at Emirates Stadium.
"For 20 years, I had to answer: 'Is that all you have to offer?' So, Sunday, it becomes an absolutely vital subject? Absolutely unbelievable," he said.
"Financially, you don't suffer any more [by failing to qualify]. During the period when we had to pay the Emirates Stadium off, the income of the Champions League was absolutely vital. But it does not have the financial weight that it had before because television money has gone up.
"It's more the fact that we want to play in the best competition but did Chelsea play in the Champions League this year? Did Liverpool? No. If we have to cope with it, we have to cope with it."