The Dutch striker has decided not to extend his Arsenal contract beyond next season, and would be available on a free transfer when his contract expires in 12 months time.
Arsenal could sell the striker this summer, and recoup a fee, or keep the forward until his contract runs out, and risk losing him for nothing at the end of next season.
Van Persie was the Premier League's top scorer last season, as the former-Feyenoord striker fired in 30 goals, helping Arsene Wenger's side overhaul north London rivals Tottenham Hotspur to finish third.
Newly-crowned champions Manchester City, as well as Manchester United and Juventus have all been linked with the star striker, and Arsenal are understood to have received a number of bids for the Dutchman since he revealed his desire to move on.
Van Persie returned to training this week, but, perhaps tellingly, was left out of Arsenal's kit catalogue advertising their new purple and black away strip. The 28-year-old is set to sit down with Wenger and Arsenal CEO Ivan Gazidis again later this week, with a decision expected on his future by Saturday.
Arsenal are believed to be unwilling to entertain offers below £25million, but with bids on the table, and van Persie keen to move on, they could look to cash in while they have the chance.
On the other hand, Arsenal will feel as though they are in a strong negotiating position. The Dutch striker is coveted by a number of clubs, which should push his price up, and the Gunners could always stand firm and keep the forward until the end of his contract.