Nketiah was reported to be on the wanted list of Vieira by a number of sources, including the Evening Standard.
The young striker, who is in the final six months of his contract at The Emirates, has been linked with a number of clubs including Newcastle, Brighton and Bayer Leverkusen.
But Palace were leading the race after entering discussions over a move for the player, according to The Times.
However, Gunners boss ended hopes of a move for the 22-year-old striker on Wednesday.
Instead Arteta allowed Folarin Balogun leave on loan for Middlesbrough and made it clear Nketiah was staying put.
“He’ our player and he’s going to stay with us,” said Arteta.
The news will have come as a blow to former Arsenal midfielder Vieira. But he refused to admit as much on Thursday.
Vieira, talking ahead of Palace’s trip to Brighton on Friday, said: “I have nothing to say about him.
‘No comment’ on Nketiah
“He is an Arsenal player and his manager makes it clear he will stay at Arsenal. I have nothing to comment.”
Asked about potential January recruits, Vieira said: “We never spoke about numbers. We try to improve the squad. We talk about which part of the team and the game that we need to improve.
“I spoke a lot with the chairman and Dougie about the feeling I have and what we are missing and what part of the game we need to improve. If it happens it is good but if it doesn’t I’m happy with the players.
“Every manager will evaluate their squad in this month and what are we need to improve. One of them, looking at the Millwall game, and how young and inexperienced we can be at times, we need young players supported with experience.
“We like to have different characteristics in different positions.”
Meanwhile, Palace will be without James Tomkins and James McArthur due to injury at Brighton.
First-choice goalkeeper Vicente Guaita sat out last weekend’s FA Cup win over Millwall but is expected to be fit enough to start at the Amex.