Killorn, 26, scored 14 goals and 40 points in 81 regular-season games last season, and five goals and 13 points in 17 Stanley Cup Playoff games. He was third on the Lightning with nine goals and 18 points during their run to the Stanley Cup Final in 2014-15, when they lost in six games to the Chicago Blackhawks.
"We're very comfortable doing a long-term contract at the right cap number with Alex," general manager Steve Yzerman told the Times. "He's been with us his entire career. He's a high-character young man, tremendously fit, and part of the core of our team. We're trying to keep the core together as much as we can."
A third-round pick (No. 77) of the Lightning in the 2007 NHL Draft, Killorn has 53 goals and 138 points in 272 regular-season games, and 15 goals and 33 points in 47 postseason games.
"He's a very reliable, very useful in all situations player," Yzerman said. "He can play right wing, can play left wing, can play in all spots. He's played very well in the playoffs for us. ... One thing that was important to Alex is he wants to play in Tampa and he'd like a long-term deal. And we were able to work it out."
The Lightning have not yet signed restricted free agent forwards Nikita Kucherov and Vladislav Namestnikov, or defenseman Nikita Nesterov.
"There's obviously still a couple guys that need to be signed, but it seems like most guys want to be here and want to be a part of this," Killorn said. "Everyone really believes in the management and what they're doing, so we're just excited for the future."
Namestnikov has an arbitration hearing on July 29.
"We'll certainly try to get it done before the hearing," Yzerman said. "But if we have to go, we have to go."
