The London club have experienced a tumultuous start to the season taking just sven points from a possible 21.
While captain Cesc Fabregas and midfielder Samir Nasri left the Emirates this summer, the Dutchman has reportedly hinted that he could be next through the door.
"I do not know [what I will do], I cannot predict the future," The Times quote Van Persie as saying. "Everybody makes his own history and only afterwards can you see how that went."
The 28-year-old went on to say that he wants to remain in the Premier League.
"I think the Premiership is still the best league in the world, it gives me everything I want."
The frontman moved to Arsenal six years ago from Feyenoord.