The Gunners boss is concerned that a quick turnaround from beating Crystal Palace could affect his side when they travel to Turkey
For the second year running the Premier League side have been drawn against Turkish opposition in the play-off round, with Wenger hoping to repeat last season's 5-0 drubbing of Fenerbahce.
Besiktas comfortably beat Feyenoord 5-2 on aggregate to reach this stage and the Gunners boss has concerns about the recovery time afforded to his squad ahead of Tuesday's game following their Premier League exploits, though but he remains convinced that the importance of the tie will ensure that his players are fully focused.
"We are desperate to do it because we want to play in the Champions League and we know how big these games are," Wenger told the club's official website.
"We had to give a lot [against Crystal Palace] - hopefully we will recover and be ready for Tuesday night.
"No matter what it costs, we want to go through. We have always a difficult draw; we had Fenerbahce last year, this time we have Besiktas. It's difficult."
Whether Laurent Koscielny will make the trip remains uncertain after Wenger revealed that a foot problem had flared up following the win over Palace.
If he is not fit then Per Mertesacker could be rushed back into action, having been given an extended break along with countrymen Mesut Ozil and Lukas Podolski after their World Cup triumph.
"We will assess Koscielny on Monday," Wenger added. "If he's fit and capable to play, we play him.
"It was our plan to bring the Germans back in contention for Everton [on Saturday] but, in case of emergency I will take Mertesacker."