The proposed deal will pay him about $7 million per year.
Dallas is hoping to sign two veteran forwards this week, with Corey Perry also an option, according to Darren Dreger of TSN.
The 34-year-old forward spent the first 13 years of his career with the San Jose Sharks.
Throughout his career in San Jose, Pavelski, who was named captain in 2015, was one of the team's top playmakers. He ranks second in franchise history in goals (355), third in assists (406) and third in points (761). He has tallied 60-plus points in six straight seasons and eight of the last nine.
Pavelski is coming off a season in which he recorded a team-high 38 goals and 26 assists for a total of 64 points to earn his third career All-Star selection. While he remained productive, he registered a negative plus-minus (negative-4) for the first time in his career.
With Pavelski making plays, the Sharks missed the playoffs just once during his tenure. Not only that, but they made the Stanley Cup Finals for the first time ever in 2016, coming within two victories of hoisting the Cup.
As free agency approached, Pavelski let it be known back in May that he was looking to re-sign with San Jose, per Curtis Pashelka of the Mercury News:
"Am I concerned? I don’t know. I know I'm going to be playing hockey next year. Hopefully it's going to be here. We love it here. I think something will happen, who really knows, but coming off a lot of emotions coming through the playoffs and that round, we'll sit down and take a look at what will happen here. We're going to be alright, I think, regardless.
"Yeah, I'm pretty confident. I've got a pretty strong belief system that I’ll be back here. It's just things have to work themselves out along the way. We had a lot of things going on with many different players. It's nothing I'm too worried about. My mindset really doesn't change."
However, San Jose found itself with limited cap space to work with after signing Erik Karlsson to an eight-year extension on June 17. While that didn't rule out a new deal for Pavelski, it limited the amount of money the Sharks could spend on free agents, such as Pavelski and Joe Thornton.
The Athletic's Craig Custance reported on June 28 that Pavelski had interest from "double-digit" teams, with colleague Kevin Kurz noting that same day that it appeared the veteran's time in San Jose was coming to an end.
Ultimately, he decided to move on to Dallas.
According to Custance, Pavelski's top priority in free agency was putting himself in the best position to win a Stanley Cup. And given last season's performance, Dallas found itself in the mix.
The Stars won 43 games last season while finishing the regular season with 93 points. They took down the Central Division-winning Nashville Predators in the first round before falling in the second round in seven games to the eventual champs, the St. Louis Blues.
Dallas "came off really well" in its meeting with Pavelski, per Custance. That combined with a chance to win proved to be enough to sell the longtime Shark on the Stars.