Emery was ousted in the French capital after falling out with the Brazilian star.
He is enduring a similar dilemma with Ozil, who has started just 13 of 26 league games this season. And Parlour believes the German could get Emery the sack.
Parlour said: "It's been a little bit like PSG with Neymar. Neymar ended up getting Emery the sack.
"He lost the dressing room and Neymar was pulling the strings there. Maybe it could be the same at Arsenal.
"It looks like that could happen. I go back to the dilemma of what Arsenal have got. He's on £350,000-a-week. Who is going to pay that sort of money?
"There's got to be a time in your career, when you're over 30 you know you're on a slippery slope. You have to come to a decision.
"He could stick his heels in and sit out his contract, and say 'play me when you want'. The players hold all the power.
"When you're left out you want a reaction from the player – especially from training. Show the attitude you want to get back into the team somehow.
"I don't know what he's been like in training."