The Gunners have enjoyed a solid start to the new campaign as four wins and two defeats have left them in sixth place in the table.
"I see top three for them," Pires told ZoneMixte.fr.
"The comeback of [Jack] Wilshere will be good, [Mikel] Arteta has progressed. [Olivier] Giroud, [Lukas] Podolski, [Santi] Cazorla have experience at a high level. Therefore, I think, and I hope, they will make great things."
Arsenal travel to Manchester United in the league on Saturday.