VANCOUVER — A team that has been tearing at the seams for two seasons is trying to trade a glue guy.

Respected senior defenceman Tyler Myers, part of the Vancouver Canucks’ leadership group and one of the most popular players among teammates, sat out Wednesday’s loss against the Winnipeg Jets after management reportedly presented him with a trade proposal that requires the 36-year-old to waive his no-movement clause.

As an extra skater, Myers participated in Vancouver’s pre-game warmup at Rogers Arena, potentially his final time in a Canucks jersey after he returned to his “home” province as a free agent in 2019.

Canucks general manager Patrik Allvin, who is on a scouting trip, announced about three hours before Wednesday’s game that Myers would not play due to “roster management.” The team made no trade announcements, although players and coach Adam Foote were asked about the situation after Vancouver lost 3-2 in overtime on Cole Perfetti’s goal 1:37 into three-on-three.

Most of them sounded resigned to Myers leaving.

“He’s such a big voice in the room,” winger Brock Boeser, another long-serving Canuck, told Sportsnet. “He’s a big leader and losing him will suck. He’s such a good guy, a great guy for the young guys and everyone around the rink. Personally, I think he deserves the chance to go win a Cup and just hope he chooses the right team.

“We know what’s going to happen; it’s the position we’re in. They’re going to move guys and get what they can. So, yeah, it sucks but it’s part of the business.”

With the countdown to the National Hockey League’s March 6 trade deadline ticking louder by the day, Canucks populate various media trade boards like Norwegians populate medal podiums at the Winter Olympics.

And yet, Myers’ name has been rare on these trade lists — not because the veteran isn’t a desirable pickup for teams with Stanley Cup ambitions, but because there didn’t seem much chance that the transplanted British Columbian would agree to a move. 

The 36-year-old, who was born in Houston but grew up in Calgary, has made Kelowna his home since he won the Calder Trophy with the Buffalo Sabres in 2010. Myers and his wife, Michela, have three children and the eldest, Tristan, has cerebral palsy. Myers has spoken publicly about his family.

The family is settled in B.C. and has support for Tristan.

The fact that Myers didn’t just say no to whatever Canucks management presented him is likely indicative of its potential appeal to a player whose 18-year career in Buffalo, Winnipeg and Vancouver has been played without a Stanley Cup Final appearance.

While Myers’ no-movement clause gives him a veto now, his trade protection diminishes to a 12-team no-go list on July 1 for the final season of his three-year contract. Whether he wants to be traded or not — and Myers has said he’d like to stay — the defenceman is empowered to control his destination now than he will be this summer or next season.

His departure would certainly be a blow to teammates and, especially, the young defencemen on the team he willingly mentors. Myers is frequently the veteran player Tom Willander, Elias Pettersson (Junior) and Zeev Buium approach for advice or support.

“I’m so new to this I don’t know how any of this works, but I love him,” Buium, the 20-year-old rookie, said after the game. “He’s been amazing to me since the first day I got here, texting me, making me feel comfortable. And little things on the ice, systems, getting to know me, speaks volumes to who he is as a person and a player. You can’t just play 1,100 games in this league, so he’s been awesome. Awesome to sit by him (in the locker room) and just pick his brain and hang out with him. Everyone respects him.”

“If he ends up being traded, it will definitely be a missing piece in the locker room, for sure,” Willander, another 20-year-old freshman, said. “It’s not just the knowledge he provides, but he’s also a great person in the locker room, you know? On the ice, he helps with stuff and gives me tips. But I think he’s a great person off the ice, too, and the more people you have like that in the locker room, the better. So it would definitely be a missing piece.”

Of course, other teams appreciate these pieces, too — players who bring value to a dressing room like they bring experience to the ice.

Attrition alone doesn’t explain why Myers, a free-agent signing by former GM Jim Benning, has become the third longest-serving Canuck, surviving one major regime change and four different head coaches.

Without Myers, Vancouver failed twice to hold one-goal leads against the Jets, who have under-achieved this season at least as much as the Canucks have.

Goals by Canucks Drew O’Connor and Evander Kane near the start of the first and second periods were offset by goals from Jets Kyle Connor and Gabe Vilardi. 

Goalie Nikita Tolopilo, starting for Vancouver due to Olympic bronze medallist Kevin Lankinen’s late arrival home from Italy, was the main reason the Canucks made it to overtime.

But after making big saves on Connor and Mark Scheifele in OT, Tolopilo couldn’t stop Perfetti’s point-blank shot at the end of a three-on-two rush enabled by Marco Rossi’s poorly-timed change at the end of a long shift.

Myers was replaced in the lineup by Pierre-Olivier Joseph. Willander logged 19:08 of playing time and was on the ice for the overtime winner. In his first game since suffering a facial fracture Jan. 25, Buium finished with 16:30 of ice time while second-year defenceman Pettersson (Junior) logged 19:34. Veteran Canuck blue-liner Filip Hronek led all skaters at 28:53.

Vancouver does not play again until Saturday in Seattle.

“There’s a couple ways to look at it,” coach Adam Foote said of the situation. “Obviously, as a coach, you want to have all the veteran Ds, you want to have all the best players in the world. But this is a different situation where (there is) development and. . . where this organization wants to go. It’ll get a guy like Willander, for example, more reps. Get him prepared in those situations faster to be asked to play in a place that he might not be ready to play in right now. You look at our league, guys are asked to be men before their time starts at 18, 19, 20, right? Just pro hockey, pro sports.”

Foote told reporters he was aware Tuesday night that Myers might not be available to play and was told Wednesday morning that the defenceman had to come out of the lineup. Foote said he asked Myers to take the warmup in case something happened to a teammate.

“He’s a great, great guy, a good human as you all know,” Foote said. “Really enjoyed coaching him, that’s for sure. You know, every year it seems like you lose one you like. It’s part of the game.”

The Canucks traded superstar captain Quinn Hughes to the Minnesota Wild in December, and sent leading goal-scorer Kiefer Sherwood to the San Jose Sharks in January. 

Fifteen teams sent pro scouts to Wednesday’s game.