The 31-year-old midfielder, who signed from Zenit St Petersburg in January 2009 for what was then understood to be a club record £15million, has seen his chances limited in the final season of his current deal.
Arshavin spent some time on loan at his former club last year and Wenger revealed there were no plans to offer the Russian a new deal to stay on.
"I don't think he will stay here, because he doesn't play enough," said Wenger.
"He is at the end of his contract at the end of the season, then he will decide what he will do."
Wenger, though, praised the efforts of Arshavin, whose last appearance was as a substitute in the Barclays Premier League defeat at Chelsea on January 20.
"Arshavin has shown 100 per cent commitment at absolutely every session, he has been an example for everybody," the Arsenal manager said.
"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."
Arshavin scored all four of Arsenal's goals in their 4-4 draw at Liverpool in April 2009, and also netted a late winner in the memorable Champions League victory over Barcelona at the Emirates Stadium in February 2011.