By Alison ChinFollow @@AlisonChin9
Gunners supporters were forced to stomach the departure of Robin van Persie to arch rivals Manchester United last summer and manager Arsene Wenger has yet to make a signing of equal quality or star power to the Dutchman.
The club was heavily linked with Gonzalo Higuain, who recently left Real Madrid for Napoli, and Liverpool's Luis Suarez, but Wenger has only purchased young Frenchman Yaya Sanogo in this window so far.
Parlour admitted that a few quality signings would make a huge difference to the club's season.
"The fans are really hoping that they can get a big-name signing," he told FOX Sports. "I'm still optimistic they will; still hoping they can before the window closes.
"I'm sure Arsene Wenger is trying his best to bring in a couple of real quality players to improve the squad, but they have got a good squad already. A couple of signings might be the difference between them challenging to win the league or not.
"They'll definitely be in the top four. I know Spurs [Tottenham] are getting better all the time and Liverpool are trying to improve; whether Everton will do well under Martinez we'll have to wait and see. I think they'll definitely be in the top four but if they bought a couple more players, they could even be in the top two.
"[They just need] more talent and they'll have a chance of winning the league. But at the moment, as it stands with this squad, I'll say fourth. I think Manchester City have the strongest squad, Chelsea under Mourinho, and obviously Manchester United."
Arsenal supporters have become increasingly frustrated at the club's trophy drought and refusal to sign big name players.
However, Wenger and the Gunners board have expressed optimism that things will be different this summer, prompting Parlour to believe the time is right for the London side to reclaim their mantle as contenders.
"I think Arsene Wenger has done a wonderful job," he noted. "Maybe because of the stadium move, financially they haven't been able to compete with the other clubs.
"Hopefully, they can now go back into the market.
"The good news is that there are links with Suarez now and with people like that, whereas over the last four to five years you've never heard of such links, because they couldn't afford them at such times because they had to pay off the stadium.
"That's the plus point and now they have to go and buy these players now, and if they can, I'm sure they will compete [for silverware] because Wenger is a very good manager."