“I do not know what I will do - I cannot predict the future,” Van Persie told The Times.
“Everybody makes his own history and only afterwards can you see how that went.”
Having seen former team-mates Gael Clichy and Samir Nasri move to rivals Manchester City in the summer, the Dutchman refused to rule out joining them at the Etihad Stadium.
“I do not know,” he said, “for one thing, as an indication, when I came to Arsenal we immediately beat City. But in recent years much has happened in England.
“Nevertheless, I think the Premiership is still the best league in the world, it gives me everything I want.”
The Gunners captain refused to be drawn into criticism of Arsène Wenger’s transfer policy, with many questioning his failure to secure adequate replacements for departed players earlier in the summer.
“I’m not a technical director and coach, I have no input in to it,” the forward insisted.