The former Manchester City chief was considered by ASSE as a replacement for Christophe Galtier, who chose to step down at the end of last season.
Vieira told ESPN: "As far as I am concerned, I focus on New York City. I find it flattering to have seen my name associated with Saint-Etienne or other clubs. I think it's always good.
"But it stopped there, it did not go further than that. I'm really happy here in New York, I'm really involved in this project because it's exciting what we're trying to build here."