Wenger will need to find a new assistant manager when Pat Rice retires in the summer.
Parlour wrote in the Daily Star Sunday: "Tony is a living legend at Arsenal. Some call him Mr Arsenal. And not only will the playing squad get a huge lift if he turns up at pre-season training - but the supporters will also be buoyed by his arrival.
"He is a leader of men, a motivator and knows Wenger's methods to a fault. I believe he has what it takes to make a big impact at The Emirates.
"As well as working under George Graham and Wenger at Arsenal, he has also come under the tutelage of Glenn Hoddle, Sir Bobby Robson and Terry Venables during his 66 caps for England and he has harvested some crucial input.
"I have to say that while I back Tony for the role, I also admit I wouldn't be too disappointed to see Steve Bould get the job either.
"He has achieved some amazing results with the Arsenal youngsters and many would say he deserves his chance at senior level."