'RMC Sport' has named Vieira as the frontrunner to succeed Lucien Favre at Nice with speculation suggesting that his appointment could be confirmed by the end of the week.
However, the former Arsenal target is currently employed by MLS side New York City FC and they are keen to retain his services.
They could face an uphill battle though with the aforementioned newspaper claiming that Nice's general manager Julien Fournier has already been to New York to begin negotiations with the Frenchman.
It would be a step-up for Vieira who has been tipped as the natural successor to Pep Guardiola at Manchester City, after the club shares the same owners as New York FC.