The Gunners followed up a convincing victory against Manchester City in the Community Shield with a 2-1 win over Crystal Palace on Saturday in their opening Premier League game, in which Aaron Ramsey netted a late winner.
Now they are looking to secure a place in the lucrative group stage of Europe's elite club competition for a 17th consecutive campaign, although Wenger could do without the fitness concerns that are hanging over several players, including Kieran Gibbs, Laurent Koscielny and Jack Wilshere.
"We want to be in the Champions League group stage
Besiktas had a convincing result against Feyenoord (winning 5-2 on aggregate in the third qualifying round), and so for us we have the luck to play the first game away," said Wenger, who has floated the idea of calling on German World Cup-winning trio Mesut Ozil, Per Mertesacker and Lukas Podolski for the first time this season.
Meanwhile, Ramsey admitted that Arsenal will need to improve on their performance against Palace, although he lauded the contribution of Wenger's summer recruits in that match.
"I think they have started really well
We were really solid at the back with (Mathieu) Debuchy and (Calum) Chambers, who were playing as if they'd been there for the last three years," he said
Arsenal would settle for a repeat of 12 months ago, when they beat another Istanbul side, Fenerbahce, 3-0 on the Asian side of the Bosphorus on the way to a 5-0 aggregate triumph.
With Besiktas in the process of rebuilding their stadium across the river, Tuesday's match will be played at the Ataturk Olympic Stadium, where Liverpool beat AC Milan in the 2005 Champions League final.
- Ba the dangerman -
Slaven Bilic's side, who finished third in the Turkish Super League last season, do not begin their domestic campaign until later this month, although they were convincing winners against Feyenoord in the third qualifying round, with former Chelsea striker Demba Ba scoring a hat-trick in the second leg.
"Arsenal have some of the best players in the world but we have seen on many occasions that talent doesn't necessarily mean a team will win," said the Croatian Bilic, who played in England for West Ham United and Everton.
The pick of the ties elsewhere on Tuesday sees Napoli, knocked out of a group containing Arsenal last season, entertain Athletic Bilbao.
Both clubs have yet to begin their domestic seasons, and Napoli coach Rafa Benitez may have reservations about playing Gonzalo Higuain, who returned late from his summer break after reaching the World Cup final with Argentina.
Athletic, who finished fourth in La Liga last season and are bidding to qualify for the group stage for the first time since 1998/99, have lost influential midfielder Ander Herrera to Manchester United this summer.
"He is a great player and I am sure they will miss him, but they are very strong collectively," said Benitez
"I have a lot of respect for them but I have confidence in my Napoli."
Germany's Bayer Leverkusen go to FC Copenhagen, while Salzburg host Swedish champions Malmo, the 1979 European Cup runners-up who have never appeared in the group stage, and Bulgarian upstarts Ludogorets travel to Steaua Bucharest.
The remaining five play-off first legs will be played on Wednesday, with the returns to come next midweek.
Champions League fixtures on Tuesday (kick-offs 1845 GMT):
Play-offs 1st leg:
Besiktas (TUR) v Arsenal (ENG)
FC Copenhagen (DEN) v Bayer Leverkusen (GER)
Steaua Bucharest (ROM) v Ludogorets (BUL)
Napoli (ITA) v Athletic Bilbao (ESP)
Salzburg (AUT) v Malmo (SWE)
Source : AFP
Source: AFP