The Frenchman says that the Russian will decide on his future when his contract runs out at the end of the season, but doubts that he will stay due
Reports had suggested that the Russian could be ready to retire from football at the end of the season, and Wenger hinted that the winger would not be offered a new deal at the Emirates Stadium.
"He is at the end of his contract at the end of the season and then he will decide what to do, but I don't think he will stay here because he doesn't play enough," Wenger told reporters.
"I must say publicly that I give him credit. He is working absolutely every session 100 per cent commitment and he is an example to everybody because he has been questioned about his commitment.
"If you see him every day, you would respect him for his commitment."
Wenger also insists he still has confidence in club captain Thomas Vermaelen, despite the Belgium international losing his place in the side recently with the coach preferring a duo of Per Mertesacker and Laurent Koscielny.
"Thomas is a great man and a fighter. His attitude has been marvellous," he continued.
Meanwhile, Wenger gave his verdict on the recent breakthrough in goal-line technology after Hawk-Eye won the battle to provide the Premier League's electronic system, with the 63-year-old coach seemingly supportive of the idea.
"What you want is the right decision to be made," he added.