Vigneault has emerged from a group of candidates that included former Rangers captain Mark Messier as the favourite to land the job. He interviewed at the club's organizational meetings in California and then met with owner James Dolan in New York.
A Rangers spokesman says no announcement was expected Sunday.
Vigneault was dismissed as coach of the Vancouver Canucks on May 22 after seven years behind their bench.
Tortorella spent 4 1-2 seasons with the Rangers and was fired May 29, four days after the New York was eliminated by Boston in the second round of the playoffs.