Unai Emery has already moved to bolster the ranks he inherited from Arsene Wenger, with deals done for Stephan Lichtsteiner and Sokratis Papastathopoulos.
They will add vital experience to the Emirates Stadium ranks, while Bernd Leno has been acquired to provide a reliable last line of defence between the posts.
There is, however, a feeling that even more is required, with Parlour calling for another proven performer at the very highest level to be drafted in.
“I think Sokratis is a good signing and he will be a no-nonsense, traditional defender in the mould of Tony Adams rather than someone who wants to play out from the back.
“Sokratis is very experienced and he’s a big game player with great leadership qualities. The fact he knows [Pierre-Emerick] Aubameyang and [Henrikh] Mkhitaryan so well is a bonus too.
“I think Arsenal still need to improve their defence, though, even after signing Sokratis and Lichtsteiner.
“They left themselves open far too often last season and it was their away form that cost them.
“The club needs an old school leader who will put their body on the line and demand the best from his team-mates. Chiellini would be the dream defender, though he’s getting on a bit.”
While Arsenal are unlikely to land Chiellini, they have brought in a player who has spent the last seven years playing alongside the legendary Italian in Turin.
Lichtsteiner is now 34 years of age, but the Switzerland international is expected to prove a useful addition, particularly as a right-back mentor to Hector Bellerin.
“Bellerin will learn a lot from Lichtsteiner, especially the vital art of defending,” added Parlour.
“Bellerin is great going forwards but he lacks discipline and can often forget his defensive responsibilities. That won’t be allowed to happen with Lichtsteiner in the dressing room barking in his ear.
“Lichtsteiner will demand a lot of respect following his successes at Juventus and his experience as captain of Switzerland. He’s also a leader on and off the pitch which Arsenal have badly needed the last few years.
“Bellerin has never really had competition or someone like Lichtsteiner by his side.”