The former Gunners midfielder believes that the club are in a good position to improve following their FA Cup success in May, but does not think Arsene Wenger's side are strong enough to beat Manchester City or Chelsea to the title.
"I am really pleased they won a trophy last season - that was so important for Arsene Wenger," Parlour is quoted as saying by the Daily Star. "He knew the pressure, and for the players, that first trophy is always the hardest to win.
"Hopefully they can push on now, but if you look at all the squads, Man City and Chelsea are stronger.
"I'm hoping Arsenal can be up there. I'm always optimistic, but if you were putting your money where your mouth was, you can't look further probably than Man City or Chelsea."
Arsenal begin their Premier League campaign against Crystal Palace on Saturday afternoon.