The 28-year-old has just under two years remaining on his Gunners contract and has so far not been willing to discuss a new deal.
Having recently seen Cesc Fabregas and Samir Nasri exit the Emirates, Wright has revealed that he would understand if Van Persie was next to depart.
"I wouldn't blame Robin van Persie if he left now," said Wright. "Arsene Wenger and the Arsenal board have had enough time with what's happened when other players have run down their contracts previously to have offered him an incentive to stay.
"[Van Persie], like anyone else, wants success and wants to play in finals but unfortunately for us at the moment that's not happening."
Wright was speaking after Arsenal's loss to Tottenham Hotspur in the North London derby yesterday.