The Champions League is the one major trophy that has eluded Wenger during his reign as Gunners boss. His new-look squad begins its bid to put that right with a qualifier against Turkish outfit Besiktas.
Wenger has made it clear how much importance he attaches to this game and the competition overall, per Sky Sports:
We are desperate to do it because we want to play in the Champions League and we know how big these games are.
We are desperate to go through. No matter what it costs we want to go through.
Wenger should be desperate to do well in Europe's premier club competition. The truth is it's been so long since he has.
The Gunners haven't made the quarter-final stage since 2010. In fact, Wenger's overall record with the Champions League is the classic two-edged sword.
He's been involved in the competition every season since the 1998/99 campaign. That's a commendable record and certainly no easy feat.
However, that many years of participation in the competition proper sill hasn't yielded a tournament win. In fact, one defeat in a final, plus another trip to a semi-final is all Wenger has to show for that longevity.
It's one of the great ironies that the manager most representative of continental chic and cosmopolitan flair during the Premier League era hasn't claimed the continent's most prestigious honour.
A major reason is the great irony at the heart of Wenger's stewardship at Arsenal. It's a tenure defined by the perfect marriage between Gallic guile and traditional English physicality.
The creativity and fluency Wenger's football philosophy imbues gave Arsenal the edge in the Premier League. However, in Europe Wenger's teams have often looked as though they are still playing Premier League games.
Wenger designed his great teams on speed, muscle and stylish ingenuity. They were built to outpace fellow contenders to the league title.
Yet in Europe, Wenger's teams usually look like they don't have the patience for the Champions League. They've rarely had the willingness to be cagey, a little more sly once the tournament pressure takes hold.
It's no coincidence that Wenger's most successful Champions League team was the 2005/06 vintage. That was a team built to defend and close off space by packing numbers in the middle.
It was one of the few times when Wenger relied on a true 4-5-1. That five-man midfield was perfectly balanced, particularly at its heart.
Cesc Fabregas buzzed around with impish daring as the chief creative influence. Next to him, Gilberto Silva was calmness personified as a rugged shield for the back four.
Alexander Hleb and Freddie Ljungberg were willing runners in wide areas, although Wenger did occasionally risk the pace of Jose Antonio Reyes. Even classy veteran Robert Pires modified his game, often playing a spoiling role as the closest support for striker Thierry Henry.
This was a team shaped to keep things tight and pick their moments in two-legged ties. Had Henry taken a late second-half chance in the final against FC Barcelona, a game Arsenal eventually lost 2-1, Wenger would've had the joy of lifting the trophy in Paris.
But since then, Wenger has never fielded a team as Champions League-ready. He came close in 2007/08 with another balanced squad.
Fabregas and Mathieu Flamini formed the complementary partnership in the middle. Meanwhile, Emmanuel Adebayor offered pace and power up front.
This team could pack five in central areas and use Adebayor as the focal point for breaks. Sadly, things came unhinged in a quarter-final against domestic rival Liverpool.
But it took diabolical refereeing decisions and lapses in concentration during both legs of that tie to finally force Arsenal out. A fractured version of that group actually went one better a year later but were subjected to a heavy beating by Manchester United in the semi-final, losing 4-1 on aggregate.
That game served as a capsule of Wenger's failings in Europe. United were economical with the ball and defensive in a 1-0 win at Old Trafford. However, they pressed high in the return at the Emirates Stadium and countered with pace.
United boss Sir Alex Ferguson, once the embodiment of buccaneering football, had reshaped his philosophy around the demands of Europe. Arsenal, meanwhile, still fell into the trap of passing their way into a cul-de-sac, believing their normal possession game and forward-breaking pace would overwhelm in Europe the way it had so often done at home.
The next season a Lionel Messi-inspired Barcelona dismantled the Gunners. Since then though, it's been a case of close, but not close enough.
Unforgiving draws in the last 16 haven't helped, although they've also been a result of failing to win the group. However, Arsenal have been just one goal short of beating Barcelona, AC Milan and Bayern Munich.
The Gunners have been the Champions League's nearly men. That has to change. Whether it can hinges on how convinced you are by Wenger's work to strengthen last season's squad.
The Frenchman has signed four players at a cost of £56 million, in the form of David Ospina, Mathieu Debuchy, Calum Chambers and Alexis Sanchez. Business has been done early and the latter signing is certainly a marquee one.
However, a more cynical view would say Debuchy and Opsina are merely replacements for summer departures Bacary Sagna and Lukasz Fabianski, while Chambers is a utility player, one for depth.
In that view, Sanchez is the only upgrade on last season's team. But Arsenal's primary group is not merely one player short of winning the top prizes.
A more physically imposing athlete in the middle, along with another pacy attacker with finishing guile, are needed to turn a solid contender into a formidable one.
Sanchez alone won't elevate Arsenal above European heavyweights like Barca, Munich and current trophy holders Real Madrid.
Of course, Wenger is a manager with a deep, deep belief in the quality of his players. He'll count on breakout years from young midfielders Jack Wilshere and Alex Oxlade-Chamberlain, similar to the banner season produced by Aaron Ramsey last campaign.
Perhaps Wenger is also counting on an improvement from current striker Olivier Giroud, like the one Adebayor made several years ago. Adebayor joined Arsenal in January 2006 and spent one-half season, then the entire 2006/07 campaign, learning the ropes, before exploding with 30 goals in 2007/08.
Giroud has had two full seasons with the Gunners but did improve his goal tally from 17 to 22 last season. Wenger has already challenged him to work on his movement this season, per L'Equipe (h/t Nick Wright of London24.com).
Perhaps another leap forward is coming from Giroud. That certainly shouldn't be ruled out altogether.
It's also true that when Theo Walcott is back to full fitness, he'll combine with Sanchez to create a pacy attack that will terrify any Champions League team. In playmaker Mesut Ozil, Wenger has a tournament veteran capable of outwitting any defence.
However, can this team play a measured game to negotiate a tense two-legged tie for the first time since 2010? Does Wenger have the players capable of choking off space and slowing down passing when crafty Champions League defences nullify the speed of Walcott and Sanchez?
Before things even get that far, will the Gunners, assuming success against Besiktas, break the habit of letting points slip in the group stage and finally value the advantage of a first-placed finish?
Wenger has to answer those questions to ensure a credible challenge in this season's tournament. That process begins in Turkey.
Wenger doesn't need to ignore the Premier League title race, nor should he. Arsenal will certainly be in the mix for that prize.
But Europe's biggest trophy should be Wenger's priority.