Despite this impressive form, Arsenal still remain an outside bet to collect silverware this season, and Parlour feels that the key to success will ultimately be in the players' ability to keep the faith.
"It's just about believing in themselves now, if it's a horse race then it's that last furlong and they've just got to keep going," insisted Parlour.
"With the run-in they've got, I think they've got a really good chance to win a lot of games. Their confidence is getting bigger at a vital stage in the season."
Arsenal have twice looked to be out of the Premier League race already this season, following heavy defeats to rivals Manchester United and Chelsea.
On both occasions Arsene Wenger's side have managed to claw back the points deficit domestically, and even with these high-profile defeats in mind Parlour is still hopeful of another meeting with their compatriots in the Champions League.
"It'd be great if we could get an all English final again like we did a few years ago," he added.
"You look at it and say that they are all strong teams in there now, there are no bad teams or teams where you think it'll be an easy game.
"You need a little bit of luck if you're going to win a cup competition. You need the rub of the green sometimes or you need a ref's decision to go your way.
"But I think Arsenal have the players that can do it."