The New York City FC boss was linked with the Arsenal job briefly following the news that Arsene Wenger would be moving on at the end of the campaign, but appears to have been leapfrogged in the running for that one by Mikel Arteta.
Nice are on the look out for a new head coach after Lucien Favre annunced on Saturday that he would be leaving the club, with a move to Borussia Dortmund seemingly impending.
Reports in France had stated that a deal was already done to take Vieira back to his homeland, but the aformentioned source claims that is not the case.
There remains a school of thought that Vieira is being groomed for a future role at Manchester City, with his current employers a member of the City Football Group.