The forward – a talismanic figure at Selhurst Park – is free to talk to foreign clubs this month having entered the final six months of his contract.
There would also likely be interest from a number of Premier League sides should Zaha not sign an extension, putting Palace in a difficult position.
Vieira has talked about wanting to sign the kind of players to help the club hit the “next level” but the doubt surrounding the future of such a key player could undermine such plans.
This month’s transfer window offers the last chance to bank any kind of fee for Zaha, who could feasibly walk away for free in just a few months’ time.
Speaking ahead of Saturday’s FA Cup Third Round meeting with Southampton, the Palace boss said: “We know the situation and we want to keep him. He’s an important player for the club and he’s loved here.
“We have to wait and see what he will decide to do. What matters is the commitment he is showing in the games."