"We love Kirill, I don't think there's any secret there, and what he's brought to our team," Guerin said. "We will do what we can to get a fair deal.
"We'd prefer a longer deal. There's two sides to the coin. You have to be open-minded. Like I said, it's a process, so there's some going back and forth and things like that."
Kaprizov, who was voted a finalist for the Calder Trophy as NHL rookie of the year this season, can become a restricted free agent July 28.
The 24-year-old led rookies in goals (27), points (51), power-play goals (eight) and shots on goal (157) in 55 games. He was second in even-strength points (38) and power-play points (13) and was tied for third in plus/minus rating (plus-10).
He led the Wild in goals, points, points per game (0.93) and overtime goals (two), and scored three game-winning goals. Kaprizov, who averaged 18:18 of ice time per game and had a shooting percentage of 17.2 percent, scored the most goals, assists and points by a rookie in Wild history.
"It's great to get recognized but [Kaprizov's] ultimate goal is to win and win a Stanley Cup," Minnesota coach Dean Evason said. "He says all the right things and does all the right things. I'm not surprised that he's extremely humble with that. That's what our group has tried to instill and we've made steps with that this year."
Minnesota (35-16-5) was the No. 3 seed in the Honda West Division for the Stanley Cup Playoffs. Kaprizov scored three points (two goals, one assist) in a seven-game loss to the Vegas Golden Knights in the Stanley Cup First Round.
Minnesota also hopes to re-sign pending restricted free agent forwards Joel Eriksson Ek and Kevin Fiala each to a long-term contract.
Fiala was second on the Wild behind Kaprizov in goals (20) and points (40) in 50 games. The 24-year-old scored two points (one goal, one assist) in the playoffs.
Eriksson Ek scored an NHL career-high 19 goals and 30 points in 56 games. The 24-year-old scored three points (two goals, one assist) in seven playoff games.
"We see those guys being here long-term," Guerin said. "They're part of the foundation of this organization and our team. You could see it on the ice that they're -- whether they like it or not, I know they're young players -- but they're leaders on our team. And they provided us with a lot on both sides of the puck. So, yeah, they're a priority."
Forwards Marcus Johansson, Nick Bjugstad and Nick Bonino, and defensemen Ian Cole and Brad Hunt each can become an unrestricted free agent.
"We're trying to build a team, and we're not just going around one guy," Guerin said of Kaprizov. "We have a lot of good players. We have a lot of good young players. We're trying to continue to build on our new core that's emerging, and Kirill is a part of that. It's not one guy that we just build around. We want to just try to avoid being focused on one guy. There's a lot of other pieces to the puzzles that we're going to need."
