The last time Arsenal's place in Europe's elite championship rested on the final league match was in 2006, when London-rivals Tottenham Hotspur needed only to match Arsenal's result to snap the sequence. Spurs lost to West Ham United and Wenger's run remained intact.
This year Arsenal must again rely on an upset to finish in the top four. They lie fifth in the Premier League, one point behind Liverpool who hold the last Champions League spot; third-placed Manchester City have a three-point advantage.
Liverpool face already-relegated Middlesbrough and Manchester City travel to Watford who languish 16th in the standings.
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Wenger's future at the club is uncertain. Should Arsenal finish outside the top four the "Thanks Arsene but Time to Go" brigade will be in full cry.
Nevertheless, the fast-dwindling number of Wenger loyalists will insist that this season, which could yet see the Gunners win a third FA Cup in four years, is a rare exception to the rule that 'Arsene knows best'.
They point to Wenger's track-record of 19 consecutive years of Champions league football after 20 successive top-four finishes in England's top-flight league. It is a legacy most clubs would hanker after, they say.
Manchester United, who under Alex Ferguson viewed Champions League participation as automatic, have missed out in two of the last three seasons. They must beat Ajax in the Europa League final next week to return to the pinnacle of European football after finishing sixth in the league in Jose Mourinho's first season in charge.
Liverpool have finished outside the top four in six of the last eight seasons. Chelsea, crowned champions last week, finished 10th last year.
Tottenham finished league runners-up this season but have won no silverware since the 2008 League Cup. They will be playing Champions League football next season for only the third time.
"He is the manager who gave a stadium to the club, won cups, and he has been 21 years in the job," said striker Alexis Sanchez, Arsenal's top scorer whose own future at the club remains unresolved.
"He is the creator of the stadium, the players and style of the club."
Yet even if Arsenal win the FA Cup final and deny Chelsea a "double" it will not placate the growing number who say the club has run out of fresh ideas on the pitch.
Failure to qualify for the Champions League could see Sanchez and German international Mesuz Ozil leave. With player salaries at Arsenal lagging Chelsea, City and United, the club may find it hard to attract the biggest names.
"Wenger wouldn't get (Antoine) Griezmann," former Arsenal striker Ian Wright said this month. "Why would Griezmann come to Arsenal in the current climate?
"Whether it's Arsene's fault, whether it's the people above him, Arsenal are not your first destination."
(Reporting by Martyn Herman; editing by Richard Lough)
