Wenger expects a tough test against Slaven Bilic's side, who defeated Feyenoord 5-2 on aggregate in the third round of qualifying when former Chelsea striker Demba Ba scored a hat-trick in the second leg.
But the Gunners travel to Istanbul on Monday in good heart following a dramatic 2-1 stoppage-time victory over Crystal Palace on the first day of the new Premier League campaign.
And Wenger is aware of the riches on offer for a place in the lucrative group stages of the competition, as Arsenal look for a 16th successive season in the Champions League.
"We are desperate to do it because we want to play in the Champions League and we know how big these games are," said Wenger.
"We are desperate to go through. No matter what it costs we want to go through.
"We always have a difficult draw, we had Fenerbahce last year, this time we have Besiktas, so it is difficult.
"The preparation for us was a Premier League game we had absolutely to win, that's the best preparation for confidence.
"Now the preparation will be mainly to recover and to study Besiktas."