Mertesacker and his Germany team mates Mesut Ozil and Lukas Podolski were given the extended break by Wenger after the World Cup triumph in Brazil last month with the trio scheduled to miss the first few weeks of the campaign.
However, defenders Laurent Koscielny and Kieran Gibbs suffered knocks in Saturday's last-gasp 2-1 win over Crystal Palace in their English Premier League opener meaning Mertesacker, who last week announced his international retirement, could be drafted in to play in Turkey.
"We will assess Koscielny on Monday," Wenger was quoted as saying by British media on Monday.
"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.
"Ideally he would need one more week preparation, but he's willing to play, no problem. We are a bit short."
Frenchman Koscielny drew the Gunners level on the stroke of halftime on Saturday after Brede Hangeland's glancing header gave Palace the lead at the Emirates Stadium.
The centreback played the full 90 minutes but suffered from pain in his foot, while Gibbs lasted little over an hour before succumbing to a hamstring injury.
Arsenal are aiming to reach the Champions League group stage for the 17th consecutive season.
After an impressive 3-0 Community Shield win over champions Manchester City and the victory over Palace, courtesy of Aaron Ramsey's late winner, Wenger was confident of progressing past the Turkish side.
"We are desperate to do it because we want to play in the Champions League and we know how big these games are," Wenger added.
"We had to give a lot, hopefully we will recover and be ready for Tuesday night.
"We are desperate to go through, 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."