The Gunners are about to open a new chapter after 22 years with Arsene Wenger at the helm, with the Frenchman having been famed for a frugal approach to recruitment throughout his reign.
It may be that the purse strings are loosened a little under a new boss, with Emery being charged with the task of returning the club to the top four and challenging for major honours.
The Spaniard is a proven winner from spells at Sevilla and Paris Saint-Germain, but Parlour fears the grandest of prizes in England will prove beyond him as he lacks the financial support to challenge.
The former Gunners midfielder told talkSPORT: “I would love him to do it, but I’m going to say no.
“I think Man City are going to get stronger and stronger, and I think Pep Guardiola is going to stick around.
“I can’t see who’s going to challenge them.
“Top four is going to be important [for Arsenal].
“They’ve got to get back into the Champions League, so, for me, top four will be a very successful season.”
Parlour added: “Unless there’s massive investment, the same as at Man City, [they’ll never win the league].
“Man City will go out and buy the big players. If Pep Guardiola stays around and they keep trying to make the squad better, it’s going to be very difficult.”
Arsenal’s last title triumph came back in 2003-04 when their iconic team of ‘Invincibles’ secured domestic dominance in style.
They have only finished as runners-up on two occasions since then, with a humbling period of regression endured under Wenger.
The last two campaigns have seen the Gunners lose their standing among the Champions League elite, with the club having to console themselves with Thursday night football in the Europa League.