With just 18 months remaining on his current deal, speculation has surfaced that big-spending Manchester City are planning another raid on the north Londoners, and are ready to offer the Gunners captain a bumper £41.6million deal to lure him to the Etihad Stadium.
Van Persie wouldn't be the first Arsenal player to swap London Colney for Carrington, after Emmanuel Adebayor and Kolo Toure were recruited by the Citizens, only to be followed by the arrival of Gael Clichy and Samir Nasri last summer.
However, Parlour feels that it would be disastrous for Arsene Wenger to lose another one of his key players, especially one as influential as Van Persie.
"Thierry Henry was on big money before he went, so they can do it, but it is all about the American backers," Parlour told talkSPORT. "Are they going to say we can do this or are they going to stick to the strict wage structure which every single player is happy with and we are not going to break that.
"I think they have to. He is such an important player for them and he's an Arsenal boy through and through.
"I just hope he stays and if it takes £130,000 or £140,000 a week then Arsenal have really got to think about giving it to him because he is such an important player for the future.
"He's helping the youngsters as well, the likes of Aaron Ramsey or Jack Wilshere coming through and he has been a brilliant skipper. He has got the dressing room exactly how it should be and that is important."