Former Gunners captain Patrick Vieira has also been linked with the Arsenal vacancy, while outgoing Paris Saint-Germain coach Unai Emery has not been contacted about the position.
Mikel Arteta looks to be winning the race to become Arsenal's new manager, amid reports of the players being told that he is "90 per cent" certain to take charge.More news: Stephen Piscotty Homers in First At-Bat Since Returning From Bereavement List
Press Association Sport understands a number of Arsenal's backroom staff have followed Wenger in leaving as the club prepare for life beyond the Frenchman.
Vieira is also a firm favourite with Gunners' fans, having helped drive Wenger's Invincibles team through their unbeaten league season of 2003/2004.
Pires believes Vieira remains the ideal candidate to step into Wenger's shoes at the Emirates club.More news: Meghan Markle's father to not attend Royal Wedding after staged photoshoot fiasco
Allegri and Arteta were seen as the two leading contenders ahead of Arsene Wenger's final match in charge on Sunday, but it is now felt that it would be extremely hard to tempt the former away from Turin. I think all of them could manage Arsenal.
"With Vieira - and this is only my opinion - yes".
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Meanwhile, Pires and Vieira were teammates for six years at Arsenal.