Two former club captains Mikel Arteta and Vieira, now head coach at New York City in the Major Soccer League, are among the favourites for the role.
Vieira, who is now head coach of MLS side New York City FC, was left disappointed after speaking with the club and feels the call was merely a token gesture to one of their former players.
The Independent reports that yesterday witnessed "another day of progress and productive talks between the former player and the club".
The club is not willing to match the demand of former Barcelona coach, Luis Enrique and their plan is for Arteta to focus on coaching and team selection, while Sanllehi and head of recruitment Sven Mislintat will deal with contracts and new signings.
GETTYMikel Arteta is widely fancied to succeed Arsene Wenger
Also out of the running is Hoffenheim's highly-rated young boss Julian Nagelsmann.
Wenger's assistant Steve Bould has also been offered a new role but the former defender hasn't yet given an indication of his future and is understood be weighing up an offer from recently relegated Stoke City.
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.