Though the Reds have rebuffed two bids from the Gunners already this summer, Arsene Wenger has indicated that he will maintain his side's "amicable" pursuit of the striker, who has been frustrated at not being allowed to leave Anfield for a team in the Champions League.
"If they got Suarez it would be a massive statement, it really would," Parlour told Goal. "I've always thought they create a lot of chances, Arsenal. I know Suarez does miss a lot but he also scores a lot of goals as well.
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Wenger has been frustrated in the transfer market, with only Yaya Sanogo arriving to date, while Gonzalo Higuain chose Napoli and Chelsea appear to be at the front of the queue for Manchester United's Wayne Rooney.
Bayern Munich's Luiz Gustavo is on the verge of a £17.2 million move to the Emirates Stadium, however, and Parlour thinks that it is crucial that new additions arrive before the transfer window closes.
"It a big season for transfers," he added. "Over the years I don't think its been documented that [Wenger] has had money to spend.
"I think the Arsenal fans know that he's done a great job but this year there's been reports that he's got quite a bit of money to spend to strengthen the side. If he doesn't spend it then straight away he's under pressure."