The Russian international will be out of contract at the end of the season.
"I don't think he will stay here, because he doesn't play enough," said Wenger of the 31-year-old midfielder.
"He is at the end of his contract at the end of the season, then he will decide what he will do.
"But he has shown 100% commitment at absolutely every session, he has been an example for everybody.
"He has been questioned many times about his commitment, but if you saw him every day you would respect him for what he does on a daily basis. He has been absolutely fantastic."