The former Arsenal midfielder thinks the side could do with another striker and Remy is the ideal choice.
Many are calling for Wenger to sign a new forward after it was announced Olivier Giroud will be out until the new year with a broken leg.
The Arsenal boss has so far said the club won't be signing anyone to replace the Frenchman, highlighting that Alexis Sanchez is likely to spend a lot of time playing in a striker's role, and mentioning Theo Walcott could also fill in when he returns from injury.
But Parlour has said that the club probably needed a striker before the Frenchman suffered the injury.
He told TalkSport: “Remy is probably the only option. He is not a lot of money in this day and age. You can get him for about £8million.
“Newcastle fans will tell you that, on his day, he is a very good finisher and top player. Maybe he is the man they go for. They need back-up.
“You look at Manchester City and they are so much stronger [in the striking department]. That is the difference between a side that is going to try and go a long way in the Champions League and win the Premier League than probably Arsenal in the moment.”
Remy came very close to securing a move to Liverpool in the summer only for last season's runners-up to pull the plug on the deal at the eleventh hour because of concerns with the player's medical.
Arsenal were strongly linked with Remy in the latter stages of last season and for much of the summer but nothing has materialised. Arsene Wenger seems happy with the striking options available to him. Time is running out for him to change his mind - but one thing that might put him off a deal for Remy is the fact one club has already pulled out of a transfer for him.