The Gunners host Rafael Benitez's big-spending Napoli on Tuesday night looking to record a second win in Group F, which would put them in a strong position before the double-header with 2013 beaten finalists Borussia Dortmund.
For all of his domestic success over 17 campaigns at the helm, Wenger's men have never been able to conquer Europe, losing the 2006 final to Barcelona in Paris.
The 63-year-old Frenchman, though, remains as determined as ever to complete that personal burning ambition - with Arsenal now looking set to challenge again following the club-record £43million signing of Mesut Ozil which has helped them climb to the top of the Barclays Premier League.
"It is something I miss that I will try to fight very hard to fill my CV with," said Wenger, whose last taste of silverware was the 2005 FA Cup.
"But you play against Barcelona, Bayern (Munich), Real Madrid - every year they are there with a chance.
"You always think 'let's do it' every year, and one year it will go for you, so let's hope it will be this year. The competition is higher than ever."
Wenger added: "If we get out of the group I would say we have a chance (to win the trophy).
"Dortmund played in the final, Napoli are a very good team and Marseille is not easy, so if we get out we have a chance - but what we have to show is that we have the strength.
"It is difficult to predict because after the group stage, it is a cup (competition) and then it is about who is available who is fit and who isn't. You cannot plan.
"The super favourite is Bayern - they have the same team, plus (Mario) Gotze on top. They played the final recently many times so they may be more favourites than Barcelona because (Lionel) Messi doesn't look to have the same consistent presence as before."
Wenger has played down talk of his side already being in the driving seat for the Premier League title as "absolutely ridiculous".
Asked, however, if there was any weighting on domestic or European glory, the Gunners boss replied: "You don't choose like that. You just want to do well.
"No matter what I get, I take it."
More pressing is the immediate challenge presented by last season's Serie A runners-up, who have moved to strengthen the squad significantly following the £53million sale of Edinson Cavani to Paris St Germain as Benitez brought in the likes of Arsenal target Gonzalo Higuain, Jose Callejon from Real Madrid and Liverpool goalkeeper Jose Reina.
Napoli beat Dortmund 2-1 at home on matchday one and have opened their domestic campaign with five wins and a draw from six Serie A games.
Wenger said: "Their chairman is very, very ambitious. The problem with the seeded clubs in Europe is that the team who are coming up are not seeded, but it doesn't make them less dangerous.
"That is why we are in such a difficult group. What are Dortmund doing here? What are Napoli doing here? The group is difficult.
"This is massive game for that reason. It puts us in a strong position because we have a double confrontation with Dortmund."
Wenger continued: "We will be faithful to what we do in the Champions League and try to have the ball.
"We know as well that the way we stop them from counter-attacking is vital as that is their strength."