The Gunners have been heavily-linked with a move for the England international this summer, with suggestions that they are willing to improve upon an initial £40 million bid for the 23-year-old.
Reports in recent days have claimed that Mikel Arteta's men are increasingly confident of completing a deal for the player, and Parlour has admitted that he believes it would be a smart move.
Speaking to talkSPORT, he said: “He’s young enough and he’s a good player. He’s now in the England setup as well.
"I think he’d be a decent signing for £50 million, but it is a lot of money. I don’t know how much Arsenal have got to spend this summer. There’s been lots of reports and they need quite a few players if they’re going to try and get back into European football.
"He would certainly be a good signing if they can get him. Whether they can or not, we’ll have to wait and see.
"It's a lot of money, but if you want a player so badly. I don’t think his wages would be big, so you’d be looking at over a five-year period, they ain't going to give him the money that they’d be giving an established star in their prime.”
Parlour isn’t the only Arsenal legend to have thrown his backing behind the deal in recent days, with David Seaman also telling talkSPORT that he believes the Gunners “need” to sign White this summer.