Arsenal spent over £52million on new players last summer, less than half of what Chelsea and the two Manchester clubs shed out on deals.
And the Gunners have struggled to keep apace with Chelsea this season, who now have a 10-point gap over their London rivals in the title race.
Arsenal manager Arsene Wenger could leave at the end of the season when his contract expires.
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You get into a bidding war
There are calls for the Arsenal board to begin sourcing a replacement for Wenger, with Thomas Tuchel of Borussia Dortmund and Juventus’ Massimiliano Allegri the favourites to land the job.
But Parlour is worried the new manager may not get the financial backing he needs to compete with Arsenal’s rivals.
“Will the board say ‘yes, no problem, there’s £150million? Maybe they don’t want to spend that sort of money,” Parlour told talkSPORT.
“At the end of the day it’s a business.”
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Ray Parlour says Arsenal cannot compete with the big boys anymore
Arsenal lost 5-1 to Bayern Munich on Wednesday
Manchester United spent big last summer, including Paul Pogba's world record arrival
On Wenger, Parlour added: “When he first turned up at Arsenal it was a breath of fresh air.
“Training regimes and everything. He won the double and the competition wasn’t as hard as it is now.
“He used to get gems of players. Are there now Patrick Vieiras out there now?
“You get into a bidding war. To sign the best players there is a bidding war with City, Chelsea, United and (Arsenal) can’t compete.”