Both the Gunners and their 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.
The Emirates Stadium supremo originally cast doubt over Vieira's return, revealing that he does not believe in the philosophy of re-signing players, while Tomas Rosicky's recovery from injury may mean there is no room for a new midfield recruit.
However, according to the Daily Mirror, Wenger has not yet completely dismissed the idea of bringing the Arsenal icon back to North London, saying:
"I'm not yet moving for him. But until 31st August, it's possible."
But any hope Arsenal fans have of seeing the World Cup winner donning the red shirt again now appear unlikely, after Vieira revealed that, despite offers from elsewhere, he has decided to stay at the San Siro.
"You never know what can happen, but I have made my decision. I will stay at Inter. I am fine, I have no reason for leaving," he told L'Equipe.
"The end of last season was difficult for me as the coach didn't trust me anymore. But his words have changed. I have resumed training sessions without any physical problems.
"Tottenham showed interest in me joining them. Harry Redknapp, who I respect a lot, proposed me a challenge that could have been exciting on a sporting level.
"But it would have been very difficult on a human level. For one or two seasons with Spurs I could not see me wasting nine years spent at Arsenal."
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