The 27-year-old center can become an unrestricted free agent July 1.
"We've been having ongoing dialogue with the Isles for the past three weeks on a daily basis," Tavares' agent, Pat Brisson, told the website.
Lou Lamoriello was hired by the Islanders on May 22, about three weeks ago, and was named general manager June 5 after Garth Snow and coach Doug Weight were fired.
Lamoriello said the GM and coaching change had nothing to do with Tavares.
"That certainly has not and did not enter into any of the decisions that are made," Lamoriello said.
Tavares can begin talking to other NHL teams June 24 but cannot sign until July 1. The maximum contract he could receive from any team other than the Islanders is seven years; the Islanders can offer him eight years.
Tavares was second on the Islanders in goals (37) to linemate Anders Lee (40) and in points (84) to rookie center Mathew Barzal (85) this season. Tavares has led the Islanders in points seven times and in goals three times.
"I think everyone in the National Hockey League knows about John Tavares," Lamoriello said. "He's one of the elite players, a gentleman on and off the ice. He's just a quality individual, as well as a quality player. I don't know any better way of describing him."
Selected by the Islanders with the No. 1 pick in the 2009 NHL Draft, Tavares has 621 points (272 goals, 349 assists) in 669 NHL games, and has at least 24 goals in each of his nine NHL seasons. He has 22 points (11 goals, 11 assists) in 24 Stanley Cup Playoff games; he scored in the second overtime of a 2-1 win against the Florida Panthers in Game 6 of the Eastern Conference First Round in 2016 to give the Islanders their only playoff series win since 1993.
