Oshie played for Hakstol at the University of North Dakota from 2005-08.
"I'm a Capital," the forward told NBC Sports Washington in remarks published Saturday. "That's where I'd like to be, that's where I'd like to stay. I will tell you this though, I think 'Hak' does an amazing job at building culture and tradition and I can't think of a better guy to start with an organization from the ground up and really bring that culture and tradition to Seattle. He's so good at bringing teams together and making players play for each other."
Oshie said he has not spoken to Capitals management since his exit interview following the season, which ended May 23.
"I feel pretty confident that I've proved to [management] that I should stay, and hopefully they see that I'm valuable enough to protect me (in the NHL Expansion Draft)," Oshie said. "But these drafts are always hard because you lose teammates every season, and that's always the toughest part to part ways and have to wish someone 'Good luck' somewhere else. I hope I'm staying, but it is a tough time seeing someone go."
Seattle will begin play next season. The expansion draft is scheduled for July 21, with each team's protected list due July 17. A team can protect seven forwards, three defensemen and one goalie; or eight skaters (forwards/defensemen) and one goalie.
Hakstol was hired as Kraken coach June 24 after he was an assistant with the Toronto Maple Leafs the past two seasons. He coached the Philadelphia Flyers from 2015-19 and was North Dakota coach from 2004-15.
Oshie, a native of Everett, Washington, which is about 30 miles north of Seattle, has four seasons remaining on an eight-year, $46 million contract ($5.75 million average annual value) he signed with the Capitals on June 23, 2017.
"I guess I've given thought to the possibility (of playing in Seattle), but my allegiance is here," Oshie said in May. "I've done, I feel like, as much as I can to prove that this is where I want to be. So I've got family out there, you know, that's great, but Washington (D.C.) is where I want to be. This is where I've bled and cried, everything here. And this is where I want to stay for the long term.
"People can speculate and they can make assumptions about what I want to do or what I would like, people bring up [becoming Seattle captain], that stuff's not that important to me. This is where I want to be with my buddies, with my family, my kids are growing up in schools here. This is where I love to play hockey."
Washington was eliminated from the Stanley Cup First Round in five games by the Boston Bruins.
Oshie helped the Capitals win the Stanley Cup in 2018, scoring 21 points (eight goals, 13 assists) in 24 Stanley Cup Playoff games. The 34-year-old scored 43 points (22 goals, 21 assists) in 53 games this season and four points (one goal, three assists) in the series against the Bruins.
The expansion draft will be under the same rules for the Kraken as the Vegas Golden Knights in 2017. Seattle will select one player from each NHL team, excluding Vegas, for a total of 30 (at least 14 forwards, nine defensemen and three goalies).
