"Oh, I'd love to keep him," general manager Jim Nill said prior to the Stars' 4-2 win against the Calgary Flames in Game 3 of the Western Conference First Round at American Airlines Center on Saturday.
"But he's got to look out for himself too, so I fully understand that. So we'll see if we can figure something out."
Klingberg is in the final season of a seven-year contract he signed April 17, 2015. Selected by the Stars in the fifth round (No. 131) of the 2010 NHL Draft, Klingberg has 374 points (71 goals, 303 assists) in 552 regular-season games and 35 points (seven goals, 28 assists) in 55 Stanley Cup Playoff games.
Nill said he and Klingberg's camp will talk more following the postseason. Dallas leads the best-of-7 series against Calgary 2-1 and will host Game 4 on Monday (9:30 p.m. ET; TBS, CBC, SN, TVAS, BSSW).
"Once we're all done, then we'll sit down," he said. "We have to figure out next year and we'll go from there."
The 29-year-old said in January
he felt underappreciated
by the Stars and was frustrated in the lack of contract talks with them at that time.
"Other guys have signed right before the season before. I wanted to do that as well," Klingberg said after a 3-2 victory against the Pittsburgh Penguins on Jan. 8. "Lately it has been going more quietly and quietly. For me, as a player, I don't feel that I've been appreciated in that way when we don't even negotiate. It's quiet.
"For me, as a player, my agent, we talked to Jim a couple months back. He agreed that we could start talking with other GMs and see where we were at. Negotiation-wise, the Stars have been very quiet."
At the time, Klingberg had 17 points (one goal, 16 assists) in 26 games. He finished the regular season fifth on the Stars with 47 points (six goals, 41 assists) in 74 games.
"Yeah, I'm not going to lie, it was a little bit frustrating to start the year for some time there," Klingberg said Monday. "The All-Star break was pretty good for me just to get away a little bit mentally, physically, and all that and just refocus. Look at myself in the mirror too. Since then I've been happy with my game."
Nill said he has been happy as well and that he knows where Klingberg is coming from regarding a new contract.
"John and I have had many discussions, we have a great relationship," he said. "I fully understand his point of view, he understands ours and he knows in the end, let's go play, let's have some success, and good things are going to happen and we'll deal with that after the season's over. He's been good.
"It's not easy to block that out. It's tough, and he's been a big part of our team for a long time. So I fully understand his point of view, but he's been very professional, and he just said, 'Let's go win some games.'"