The Daily Star says there is a growing feeling at the Emirates that the club needs to make a stand after the loss of several key players.
Refusing to sell Van Persie now would send a strong message to fans that the Londoners have had enough.
Manchester City, Manchester United and Juventus all want the Dutchman, but are unwilling to pay anything near the £30m Arsenal are demanding for their skipper. United's bid is understood to have been less than £10m.
If Arsenal keep him for the first half of the season they know they could still command a decent fee in January when clubs could be desperate to land a top striker.