The Gunners have only added Petr Cech to their ranks this summer, and following a shock 2-0 home defeat to West Ham, fans have become restless.
Olivier Giroud remains Wenger's only out-and-out striker in the squad, with Theo Walcott being deployed as striker this term too.
This has lead meany to call for the signing of Real Madrid's Karim Benzema - who has long been linked with a move to the Emirates.
However, former midfielder Parlour says it's simply not good enough and a Wayne Rooney or Diego Costa equivalent must be found.
He told Sky Sports: "That is a position they've got to look at. Everyone is going to jump on the bandwagon now but it's a long, hard season and there's a long way to go.
"If you look at Man City, you know Sergio Aguero is their main man, for Manchester United it's Wayne Rooney and at Chelsea it's Diego Costa. Who is it at Arsenal?
"I didn't know who would start for Arsenal on Sunday because Theo Walcott started the Community Shield. I don't think they have someone who you can say 'he's definitely going to play and he will score us goals'."
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