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The San Jose Sharks have drawn "some serious interest" from teams regarding a trade for Erik Karlsson.

"I think he would like the chance to have an opportunity to compete for the Stanley Cup, and I understand that," Sharks general manager Mike Grier said. "His timeline, where he is in his career, [it] doesn't quite match up with where we are in our process of building this thing back up.

"I've talked to a bunch of teams and ... there are some people kind of dipping their toe in the water."

The 33-year-old, who on Monday won the Norris Trophy voted as the best defenseman in the NHL, said on Sunday at the NHL Awards media day that he wanted to be traded to a Stanley Cup contender.

"I've played with too many guys throughout my career that are amazing players and should be winners and should have won that never did," Karlsson said. "I don't want to be that guy. I want to win. That's not to say that I'm going to win. I want an opportunity to win. If that opportunity is not in San Jose right now within my timeline, then that's just the unfortunate part of business. That's not to say that I don't like it there or they don't want me there or we don't want this to work. It's just that's just the way it is."

Discussing potential trades for Erik Karlsson

Karlsson, who has a full no-move clause in the eight-year contract he signed with the Sharks on June 17, 2019, said he doesn't have a preferred team in mind.

"You just have to make the playoffs and you have a chance to win," he said. "Look at [the] Florida [Panthers]. They shouldn't have made the playoffs. They did and they went to the Cup Final. They beat [the] Boston [Bruins]. We all thought Boston was going to win. There are no guarantees. I just want a chance."

Karlsson had 101 points (25 goals, 76 assists) this season, becoming the sixth defenseman in NHL history, and the first since Brian Leetch in 1991-92, to have a 100-point season.

He finished 11th in the League in points and fourth in even-strength points (74).

"What he did 5-on-5 from an offensive standpoint, the fact he's even in the top five, everybody wants to talk defense, but this guy did so many things at such an elite level that I'm not surprised he wins the Norris Trophy," Sharks coach David Quinn said.

Karlsson previously won the Norris Trophy with the Ottawa Senators in 2011-12 and 2014-15. He's the second player to go eight-plus years between Norris Trophy wins, joining Paul Coffey, who won the award with the Edmonton Oilers in 1985-86 and then again with the Detroit Red Wings in 1994-95.

Karlsson played his first nine seasons with Ottawa, reaching the Stanley Cup Playoffs five times, including advancing to the Eastern Conference Final in 2017. He was traded to San Jose by Ottawa on Sept. 13, 2018, and the Sharks reached the Western Conference Final in his first season there, falling to the eventual Stanley Cup champion St. Louis Blues in six games.

However, the Sharks have not made the playoffs since and in recent seasons have seen franchise stalwarts, including forwards Joe Pavelski and Joe Thornton, and defenseman Brent Burns go elsewhere.

Still, Grier said despite Karlsson making it public he wants to be traded, the Sharks are not just going to give him away.

"For people who think we're going to eat 50% of his contract and all this type of stuff, it's probably not going to happen," said Grier, who was named Sharks general manager July 5. "Erik's a special player. He's on the path to being a Hall of Fame player. He's healthy, I think he proved that last year. He's a special player who drives offense like not many others in this league. ... He's not someone who we're just going to toss aside and not take things into account and try and help the organization out."

NHL.com independent correspondent Chelena Goldman contributed to this report