The former midfielder is anticipating a tough game against Watford this weekend.
Arsene Wenger's side were strongly backed to be title contenders in this campaign following a fine finish to last season that saw them secure a second successive FA Cup triumph.
A disappointing summer in which they only signed Petr Cech from Chelsea followed, though, leading many to believe that they were short of a squad capable of challenging for the title.
They are, however, now second in the table after eight games, and Parlour thinks they can be contenders as long as they are still in the mix come the run in from March or April.
"I think the most important thing for Arsenal is being involved around March or April time to be in with a chance of winning it," Parlour told Sky Sports.
"Over the last few seasons they've seemed to drop off. Everything is going well for Arsene [Wenger] at the moment but the key is keeping players fit, (if they do) I think they'll have a good chance this year.”
Tough game against Watford this weekend
Arsene Wenger’s side were in highly impressive form before the international break, securing a 3-0 win against Manchester United, with all of their goals coming in the first 20 minutes.
It was a highly accomplished performance from the side, who travel to Vicarage Road on Saturday to take on a Watford outfit who have adapted well to life in the Premier League.
And Parlour says they will need to be tougher away from home than they sometimes are if they are to put down a serious title marker, starting with this weekend.
"It was a huge game against Manchester United, bouncing back from Olympiacos, they had to get a result and start quickly,” he added.
"It's going to be tough, Watford are very resilient and tough to beat. It's away from home where you've got to be a bit tougher at times and stick in there. But I expect them to get all three points."