National media in the past week or two said Dallas and Klingberg's agent hadn't spoken in quite some time. Saad is saying today that the sides did speak about an extension recently, but they didn't make much progress in closing the gap.
Take it however you like, but he seems to suggest that Dallas is interested in a contract. He didn't use this example, but it may be similar to the Lindhom negotiation where the term is the major sticking point, and I believe Marek suggested that as well several months ago.
Because he was not traded, only the Dallas Stars can offer an 8-year contract now unless it's a sign-and-trade after the season (and that can only happen prior to the start of free agency. That seems very unlikely.
I'd be pretty surprised if a team didn't step up with a rather significant 7-year offer like NJ did for Hamilton. Klingberg's age makes it maybe less likely, but Seattle seems like a reasonable candidate. I would not be optimistic that Dallas and Klingberg find a number that is comfortable for both sides. I think the most optimistic thing to hope for is that Seattle would value the 8th year enough to do a sign-and-trade sending a mid-round pick to Dallas.