Martinook scored 13 points (four goals, nine assists) in 44 regular-season games this season and had three assists in 11 Stanley Cup Playoff games.
The 28-year-old, who can become an unrestricted free agent July 28, said June 11 he'd like to re-sign with Carolina.
"I came here three years ago and felt I was part of the culture change a little bit," he said. "I can put a little feather in my cap for that. There's a group of us who have been here for three years who have been the driving force of trying to turn this thing this around. I think we have. I want to see I through."
Martinook was acquired by the Hurricanes in a trade with the Arizona Coyotes for forward Marcus Kruger on May 3, 2018. He signed a two-year, $4 million contract ($2 million average annual value) on Jan. 29, 2019.
The Hurricanes, the No. 1 seed in the Discover Central Division, defeated the No. 4 Nashville Predators in six games in the best-of-7 Stanley Cup First Round this season before losing to the No. 3 Tampa Bay Lightning in five games in the second round.
"I think we're right there, we're so close, and if I were to go somewhere else it would be tough to see if they were to win here because I'd feel I was a big part of it," Martinook said. "At the end of the day it's a business. I want to stay here, I just had a baby girl and I have to look out for myself and my family. At the end of the day, I want to be a Hurricane and hopefully we can make that happen."
