Flames general manager Craig Conroy said the goal is to keep Lindholm.
"We're just talking to him and talking to his representation and just moving forward," he said. "Everybody wants something to be quick, but it's just been a slow process. We're going to continue to work at it.
"He's open to it. Now it's just a negotiation. It never goes quite as quickly as everyone would like. We're just in that process. The one good thing is these are all good guys, they're all happy to be here, there's no issues with that. That's the one thing. They're not saying, 'Hey, I'm not coming to camp,' or 'I'm unhappy.' With Elias, we're working on a deal. That's where it is. Can we get something worked out? That's really the main focus right now."
Lindholm is one of six Flames who can become a UFA at the end of the season, along with forward Mikael Backlund and defensemen Noah Hanifin, Nikita Zadorov, Chris Tanev and Oliver Kylington.
"Lot of guys on one-year deals," Lindholm said. "We're just focusing on the season. That's all I can do. Try to be competitive out there and have a good season."
The Flames (38-27-17) finished two points behind the Winnipeg Jets for the second wild card into the Stanley Cup Playoffs from the Western Conference last season. Conroy was promoted to replace Brad Treliving as GM on May 23, and assistant Ryan Huska was named coach June 12, replacing Darryl Sutter.
"It's exciting," Lindholm said of the changes. "I know Huska, he's been around on the bench for a long time. He's a great guy. Haven't had him as a head coach but you know where he's at. … We're excited, and he's a great guy. 'Conny' has been around a long time too, so we're excited."
Lindholm said he feels good about the Flames' playoff chances despite all the changes and contractual uncertainties.
"We still have pretty much the same team," he said. "We had some good moments in the season last year. We just have to string it all together and be more consistent. We have some really good players and we have to be more consistent. I'm excited about the season. You always say once you get in (to the playoffs) you never know. You look at Florida, they got in in the last second there and almost made it the whole way.
"Last year we were coming in with a lot of expectations, and on ourselves as well. Didn't live up to them but still pretty close to making the playoffs. We still have the same team. Maybe it's good for us to be a little underdog here."