And it is also understood the club will hold talks with interim manager John Carver in the next few days to clarify his position at St James??? Park.
Vieira, who is currently an elite development coach at Manchester City, had been a strong candidate to take the job as his first in club management.
The former Arsenal and France midfielder is keen to manage in his own right and had been identified by Newcastle as fitting their criteria of a young and progressive head coach.
But he will now no longer be considered for the role.
If the club decide to make an external appointment and not keep Carver in charge, it is believed Steve McClaren will be a leading candidate.
McClaren is available after being sacked by Sky Bet Championship club Derby County last month.