The Flames, who had their best regular season (50-25-7) since 1988-89, when they won their only Stanley Cup championship, were eliminated in the Western Conference First Round in five games by the Colorado Avalanche.
Tkachuk had three points (two goals, one assist) during the Stanley Cup Playoffs.
"He's a heart-and-soul guy," Treliving said. "He comes with leadership ability. That's sort of part of his DNA, but that's grown in his three years as a pro. It's amazing that three years have already gone by. He's an integral piece of this team."
Tkachuk, who has 174 points (71 goals, 103 assists) in 224 NHL games, is part of a group of NHL restricted free agents that includes forward Mikko Rantanen of the Avalanche, forward Patrik Laine of the Winnipeg Jets, center Brayden Point of the Tampa Bay Lightning, and forward Mitchell Marner of the Toronto Maple Leafs, among others.
"That's been talked about a lot this year," said Tkachuk, who has no expected timeline on a new contract. "No matter who is playing well out of the restricted class, it seems like every time somebody's playing well they somehow talk about everyone else in the class. It was hard to avoid questions like that this year. You don't want to talk about it. You're watching TV and hearing stuff. The season's over.
"Now you start thinking about it more and try to figure something out."
Neal, who signed a five-year contract with Calgary on July 2, 2018, had 19 points (seven goals, 12 assists) in 63 regular-season games and was a healthy scratch in Game 5 against the Avalanche.
"I don't think it takes a rocket scientist to sit up here and say this is not exactly how we projected things to go," Treliving said. "James didn't sign here to be a scratch in Game 5 of the first round.
"There's two parties involved in it. There's the player and the team. We both want him to be successful. How do we get to that end goal? I think he's real committed to obviously having a better year next year."
The 31-year-old forward has 270 goals in 766 NHL games and 31 goals in 104 Stanley Cup Playoff games.
"I want to be a top-six guy who is counted on to score big goals and be an impact player," he said. "I've been like that my whole career. I've scored 20-plus goals in every one of my years except this year. I know I can get back to being that type of player and help this team out."
Addressing the goalie situation will be another focus for the Flames in the offseason.
Mike Smith, who was 23-16-2 with a 2.72 goals-against average and .898 save percentage in 42 regular-season games, started all five games for the Flames in the playoffs, going 1-4 with a 3.20 GAA, .917 save percentage and a shutout in Game 1. The 37-year-old can become an unrestricted free agent July 1.