The north London side are aiming to try and secure qualification for next season’s Champions League after having finished outside the top four places in the table in the last two seasons running.
The Gunners ended up in sixth place in the Premier League table and without a trophy last season under Arsene Wenger before the Frenchman decided to step down at the end of last term.
Unai Emery has been tasked with steering the north London side back up the Premier League table as they look to try and establish themselves as serious contenders for a top-four finish.
The Gunners have only won one of their opening three games in the Premier League this season but they will be aiming to make it back to back victories when they take on Cardiff away from home on Sunday.
And Arsenal legend Parlour believes that the north London side are facing some stiff competition in trying to break back into the top four this season.
Speaking in an interview with the Daily Star, Parlour said: “I’ll be delighted if they finish fourth.
“If they come fourth it’s been a very, very good season, a successful season.
“That’s how hard the Premier League is now and the competitive nature.
“Top four will be difficult – the bookmakers don’t get it wrong too often and Arsenal are the sixth favourites to get to the top four.
“In that respect it would be a good season. I’m always optimistic they can have a good season.”
Arsenal have not won the Premier League since 2004.
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