The 29-year-old defenseman, who can become an unrestricted free agent on July 13, has played all eight of his NHL seasons with the Stars since they selected him in the fifth round (No. 131) of the 2010 NHL Draft.
"At the end of the day, I always want to stay here," Klingberg said Tuesday, two days after a 3-2 overtime loss to the Calgary Flames in Game 7 of the Western Conference First Round. "This is the only team I've been talking to, obviously. With [Stars general manager Jim Nill], and on our side, we've been trying to find different ways to get it done. Year length, money-wise, just trying to get something we're both happy with."
Klingberg, who is in the final season of a seven-year contract he signed on April 17, 2015, has 374 points (71 goals, 303 assists) in 552 regular-season games with Dallas, and 35 points (seven goals, 28 assists) in 59 playoff games.
Nill said last week that he'd "love to keep" Klingberg but reiterated Tuesday that it would come down to terms.
"John has an opportunity to be a free agent, and I don't blame him," Nill said Tuesday. "He's got to look after his family. He'll see what the market is, and we'll see what the market is, and get a feel for that and see if it's a fit for both parties. It all depends on term and money. He knows where we're at, I know where he's at. He's earned this right, and I give him full credit for that."
Klingberg's next contract is one of many decisions Dallas faces during the offseason.
Another is that of coach Rick Bowness, who had his two-year contract expire at the end of the season.
"The playoffs bring out your passion," Bowness said. "That excitement, that pressure and everything, that's what we live for, what we sign up for. There's still lots of fire left in me."
The 67-year-old was named Stars coach on Dec. 10, 2019, replacing Jim Montgomery. Nill said Bowness has faced a lot of adversity since stepping into the role, including a season shutdown due to COVID-19, a run to the Stanley Cup Final during the bubble in 2020, and another shortened season further compacted by a COVID-19 outbreak and ice storm.
"He's handled the situation well," Nill said. "We had 98 points this year. That's a pretty good year. So he's done a good job. We'll sit down with [ownership] and reassess everything over the next five or six days, and go from there."
For his part, Bowness said he is not yet ready for retirement, even if he does not get the opportunity to coach in Dallas next season. He is 212-351-28 with 48 ties in 12 NHL seasons as a coach with the Winnipeg Jets, Boston Bruins, Ottawa Senators, New York Islanders, Phoenix Coyotes and Stars, and 26-23 in 49 playoff games.
"[The Stanley Cup] is still the driving force," Bowness said. "But as you get older, you also want to leave an impact on the game, and that legacy becomes just as important to me. Do I want a Cup? Absolutely. Is it going to define me? No. I won't let it. Being an impact on their lives, and not just being a coach and trying to make them better, that means more to me than having my name on the Cup. It does."
The Stars also issued several injury updates: center Roope Hintz missed Game 7 of the first round because of an oblique strain sustained in Game 6, center Tyler Seguin fractured his foot in Game 1, and center Luke Glendening sustained a knee injury and experienced concussion symptoms after a hit from Flames defenseman Nikita Zadorov in Game 6.
Each is not expected to need major surgery and is expected to be healthy for the start of next season.
