Coincidentally, Alain Vigneault, who was fired by the Canucks last month, is interviewing for Tortorella's old job with the Rangers, also on Tuesday.
Vigneault is in La Quinta, Calif., to speak with Rangers brass at the team's annual organizational meetings.
The Rangers gave Vancouver permission to speak with Tortorella, who still has two years remaining on his contract with New York. Before his somewhat unexpected dismissal less than two weeks ago, Tortorella had signed a contract extension during the season.
Tortorella also is on Dallas' radar as the Stars conduct a coaching search to replace Glen Gulutzan. As of Monday, the Stars had not requested permission to speak with Tortorella, though the Rangers are not expected to stand in his way should they make that request.
The fiery Tortorella led the Rangers to the Eastern Conference finals last season, but saw his team make a disappointing second-round exit this spring. Rangers general manager Glen Sather declined to explain why he chose to fire Tortorella, though it is believed that his brash, abrasive coaching style took its toll after four years in New York.