Vieira, captain on Wenger's iconic Invincibles side, was mooted as an early contender but reports on Tuesday claimed the New York City FC manager felt disappointed, under the impression he had been considered an afterthought by the Arsenal board.
Sky sources understand Vieira's former team-mate Thierry Henry has not been contacted about the vacant role.
GETTY Mikel Arteta was emotional after his last game for Arsenal
Another candidate was Hoffenheim's Julian Nagelsmann, but the German club recently insisted he will still be their manager next season.
Frenchman Pires - who enjoyed a successful six-year spell at Highbury before joining Villarreal in the summer of 2006 - believes all of the names linked could take on the role, but is in no doubt of the man he would like to see succeed Wenger.
The Spanish midfielder has been sidelined at Arsenal for 18 months with a serious ankle injury but the Independent says he "could be offered a new player-coaching deal" next season - if he wins his fitness battle.
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