Arsenal are in the market for a creative midfielder and lost Martin Odegaard earlier this summer when his loan deal expired.
The Gunners are looking at additions and Maddison is believed to be a player the north London club are considering signing in the ongoing transfer window.
Leicester could be open to selling him as Maddison’s influence waned last season, but Parlour indicated that he could be out of Arsenal’s budget.
He is also not certain whether the midfielder would want to leave Leicester, who are expected to further bolster their squad this summer under Brendan Rodgers.
The Arsenal legend does not believe that the Gunners have the finances to spend £60m or more to snare Maddison away from the King Power Stadium this summer.
Reacting to the rumour, Parlour said on talkSPORT: “The problem is the price tag.
“Leicester want top money for him and would he want to leave Leicester?
“Brendan Rodgers will be backed.
“If he needs money to spend to bolster the squad, the owner will say, no problem and here we go.
“So, would he want to leave Leicester? That’s the big question.
“He is going to be worth £60m or maybe more. Maddison is a great player, he really improved Leicester.
“I know for a fact Arsenal are looking for a number 10 and a striker at the moment.
“Leicester will probably price him out of the market from Arsenal’s point of view and they might have to look elsewhere.”
Arsenal have already spent £50m on signing Ben White from Brighton and it remains to be seen how much more money they have to spend.