Unai Emery is looking to make the Gunners tougher to break down, with a soft centre being exposed again at the start of a 2018-19 campaign which has seen five goals conceded in two games.
Xhaka is intended to be a shield in front of the back four, while also providing a link between defence and attack.
Parlour, though, has suggested that the 25-year-old is struggling to fill the role expected of him, with summer signing Lucas Torreira waiting in the wings to take his place.
The former Arsenal midfielder told The Sun : “Xhaka does tend to give the ball away a bit too much in this new system of playing from the back. And he needs to be more mobile if he can.
“But he has to learn to deal with having the ball in those areas. Compared to Matteo Guendouzi, who impressed in pre-season, he is not as energetic or mobile.
“If he’s not doing his job, Emery has already shown him that he will be taken off — he did it to him against Chelsea at half-time.
“And with Lucas Torreira, who I think sooner or later will start after being bedded into the side, Xhaka could be left out.”
Parlour added on a man signed from Borussia Monchengladbach for £30 million ($38m) in the summer of 2016: “Xhaka looked to have a good World Cup, so it’s hard to say what’s wrong with him now.
“He looks like a guy who takes a bit of time to get back into the rhythm of playing week in, week out after a break, especially with the new manager.
“But there are players breathing down his neck. If he doesn’t do his job, he won’t be in the team.
“The form players deserve to play. He has to knuckle down and he has to play well.”
Aaron Ramsey is another of those pushing for starting midfield berths, with the Wales international having been benched for a 3-2 defeat at Chelsea.
The 27-year-old is yet to commit to an extension at Emirates Stadium , as he heads towards free agency in 2019, but Parlour believes he will continue to be a key figure under Emery.
He added: “I know Aaron as a person and he will not be worried about getting dropped or the contract situation.
“He will be getting his head down and waiting for his opportunity.”