The Gunners beat Newcastle 2-1 at St James' Park in their last Premier League game before the international break to leave themselves in third spot in the table, trailing leaders Chelsea by seven points.
Arsene Wenger's men look set to clinch a Champions League berth this term, something that has become customary during the French tactician's 18-and-a-half-year tenure in north London.
But Gould, who scored 23 goals in 83 appearances during his two-year spell with Arsenal, believes his former employers still have an outside chance of lifting their first league title since 2004.
Gould, who was speaking ahead of the Bristol regional heat to find the 'People's Pundit' championed by Carlsberg, the official beer of the Premier League, exclusively told Express Sport: "They're up there. I have the utmost respect for Wenger and for what he has achieved. The FA Cup win last season was a wonderful achievement.
"They needed that. They are so well supported.
"I saw Arsenal playing against Anderlecht earlier in the season at the Emirates and they have some magnificent players but it is difficult getting that XI out on the pitch at the same time."
Gould believes that Wenger will stay at the Emirates for another season and expects him to strengthen his defence when the transfer window reopens in the summer.
He added: "Hopefully, they can shut the door at the back for the next couple of months, and if they can do that, I'm sure Wenger will remain as the manager and he will buy some defenders that are top class."
Arsenal host Liverpool in their first league game after the international break next Saturday (12.45pm).
The mission of the Carlsberg fan squad is to make football better for fans. That's why, If Carlsberg did Pundits…they'd probably be just like you. Carlsberg and talkSPORT have joined forces to give one fan their big break on national radio and next Thursday sees the potential pundits face off in Bristol. If you fancy watching our pundits take each other on, alongside Bobby, head to the V-Shed, The Waterfront, Canons Road, Bristol at 8pm. Find out more at #PeoplesPundit