Under normal circumstances Arsenal would not begin talking about another new deal until the season after next and Highbury decision-makers are keen not to break that pay review policy.
Wenger said at the weekend that he is confident Vieira will stay and challenged the 28-year-old to reaffirm his commitment to Arsenal.
"For me, Patrick is staying," he said. "But we want him to be committed. If there was a bid of £20million or £30m, could we really say no to it? Of course we could."
Wenger, meanwhile, is looking to sign two more players. Dutch striker Robin van Persie and Spanish goalkeeper Manuel Almunia have already been recruited and it was thought they might be the only fresh additions to the squad.
Cover for centre-back duo Sol Campbell and Kolo Toure will top Wenger's wish-list but the Arsenal boss is refusing to reveal the position of his transfer targets.
"There is still a possibility someone will come in soon. One or a maximum of two," he said.
Ray Parlour could be on his way from Highbury after being offered a long-term deal and the chance to play regular first-team football with Middlesbrough.
Arsenal beat Barnet 10-1 in their opening pre-season game on Saturday, with van Persie scoring one of the goals. Spaniard Jose Antonio Reyes and Francis Jeffers both hit hat-tricks.
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