The Gunners' arch-rivals, Tottenham Hotspur, have been strongly linked with a move for the 33-year-old Frenchman, who made more than 250 league appearances and won three Premier League titles and four FA Cups during his time at Highbury.
However, speaking in Beijing during the Barclays Asia Trophy, Spurs boss Harry Redknapp admitted that talks had stalled over a potential deal.
And it then emerged that Arsenal were believed to be weighing up a move to bring the iconic central midfielder back to the club following a four-year absence.
But the Emirates Stadium supremo has now cast some doubt over Vieira's return, revealing that he does not believe in the philosophy of re-signing players, and adding that Tomas Rosicky's recovery from injury may mean there is no room for a new recruit.
"I have a general policy about re-signing players but I never said I would never do it," he said.
"I am not a big fan because I feel once the players have gone, they have gone.
"Two weeks ago I didn't know if we would have Eduardo or Rosicky and they are both completely back so that makes the squad quite big.
"I don't know it could have psychological impact on the rest of the squad."
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