Palace's top scorer netted his 11th of the season in the 3-0 win over Arsenal on Monday night, which only poured more fuel on the transfer rumour fire, with many Gunners fans believing Zaha would be a perfect addition to their youthful squad.
Zaha's contract is moving into its final year at Selhurst Park and Arsenal could be tempted to make a bid for the Ivory Coast international, someone they failed to land three seasons ago when he'd put in a transfer request.
"He's been linked after the game? There is no truth about that," Vieira insisted.
"Of course (we want to keep him). I believe Wilfried is an important player for the team and for the football club.
"He's a really good inspiration for the young players that we have. He knows this club better than anybody else and when he is performing like that, you know you only want to keep your best players and he is one of them."
Zaha also talked about the importance of the squad not playing the badge on the shirt and instead believing they can impose their game on anyone.
Vieira added: "I think that is a really strong quote by Wilfried. This is why those kinds of players who have a strong personality and have experience, have a lot to give to the squad, especially to the young players.
"It is about the quality and the determination and how much you are prepared to fight on the pitch as well. I think that is really important for him to come and express that kind of quote. This is the truth.
"We want to compete against any team and on the field we are 11 against 11. Of course there are teams who have a really good squad, but we can compete and this is what we want to do. To compete against those teams."
The victory over Arsenal moved Palace onto 37 points, which in the last five seasons has been more than enough to secure their Premier League status.
"From the first day I really believed about the potential of the squad and we never talked about safety. We always talked about how do we want to perform as a team and how - if we want to win matches - we have to perform," Vieira said.
"It wasn't in my head to start the job talking about safety. This is something that I don't have in my mind and I don't want players to have that in their mind."