The two sides are "closing in" on a deal worth $30 million, according to TSN's Frank Seravalli.
The free-agent market opens Monday at noon ET and Myers is one of the top defenders available. The 29-year-old had nine goals and 31 points in 80 games with the Winnipeg Jets last season.
Myers was a first-round pick, 12th overall by the Buffalo Sabres in 2008. He has 74 goals and 265 points in 635 career games.
The Blue Jackets are making a last-minute pitch to Artemi Panarin with hopes of keeping him in Columbus.
The club's offering the star forward an eight-year deal worth at least $96 million, according to The Athletic's Aaron Portzline, and the contract could be worth as much as $100 million.
However, in order to lock up Panarin for eight years, the deal must be agreed upon and signed by midnight ET on Sunday. If Panarin hits the open market Monday, the longest contract he can sign is seven years, with any team, including Columbus.
The Blue Jackets reportedly made an eight-year, $72-million offer to Panarin last summer, but he informed them he wasn't interested in negotiating an extension.
The Russian winger led Columbus in scoring in each of his two seasons with the team and tallied a career-high 87 points this season.
With reports of Matt Duchene signing with the Nashville Predators and netminder Sergei Bobrovsky likely headed to the Florida Panthers, the Blue Jackets are taking one last swing at keeping one of their most promising talents.
Dach entered the draft as the third-ranked North American skater, and he has all the tools to become a prominent NHL center. He likely won't jump straight to the big leagues out of junior, but Dach immediately upgrades Chicago's prospect pool.
The Alberta native possesses soft hands and strong skating ability that's rare for a player his size. He should pay off to be a smart pick at No. 3.
What they're saying
"He's huge, he's strong on the puck, he handles it well in tight (rare for a player his size), he's a better skater than he gets credit and his length makes him a lot to handle when he drives the net (which he needs to do more often) or controls the puck on the cycle. He's also a player coaches lean on defensively because he uses his stick effectively to disrupt plays and win battles." - The Athletic's Scott Wheeler
Only three European skaters were ranked higher than Heinola on NHL Central Scouting's final list, and The Athletic's Corey Pronman had the blue-liner slotted in at No. 28 overall on his draft board in May.
In addition to notching nearly half a point per game in his first year in Finland's top league, Heinola helped his home nation capture gold at the 2019 World Junior Championship. He also represented his country at the 2019 Under-18 worlds and the 2017 Under-17 Hockey Challenge.
Heinola produced nine points in as many games for Lukko's junior squad in 2018-19 before being promoted to the big club.
What they're saying
"Heinola is a calm, poised puck-moving defenseman who generates clean exits and entries with his vision, and makes plays on the man advantage," Pronman wrote in May. "He’s fine defensively due to his positional play, despite not being the biggest defender. However, he has limitations that may hinder him as he progresses.
"His size is obvious but his skating is also a minor concern. His stride breaks down when he gets going in a straight line, which is worrisome in a 5-foot-11 defender. I like his edges a lot, with Heinola showing a powerful burst on his first few steps to balance out the stride issue somewhat."
Soderstrom has the potential to be a special player. His game is perfectly built for today's NHL. As a right-handed, puck-moving defenseman, he'll be a highly coveted commodity. His stats don't jump off the page, but that's because he was a 17-year-old playing against grown men in Sweden's top professional league.
He's your prototypical Swedish blue-liner. He's a smooth skater, calm with the puck, and makes an excellent first pass. After moving the puck, he loves joining the attack. He's not afraid to get creative at the point as the last man back. It can get him into trouble at times, but he has the quick hands to make plays that other players could only dream of. Adept at quarterbacking a power play.
Soderstrom gets it done on the defensive end as well. He isn't very physical, but has a good stick, closes gaps well, and can read plays.
What they're saying
In an exercise with The Athletic's Craig Custance, an amateur scout was asked to draw comparisons between draft prospects and current NHLers. For Soderstrom, the scout decided on Nashville Predators captain Roman Josi.
"He’s another offensive player. He’s not Erik Karlsson. How offensive is he going to be? Who knows? He’s reliable. He’s dependable. He could be top 10 in the draft. He could be the second D off the board. Josi is a pretty good all-around defenseman who has some offense, too."
Hughes has elite short-area quickness, hands softer than butter, and a sky-high hockey IQ. He'll be a dynamic, playmaking offensive threat the minute he steps on the ice for his first NHL game, and has the potential to become a franchise player. Don't be fooled by his small stature.
Kaapo Kakko - Right Wing, TPS Liiga (Finland)
With such an impressive resume, Kakko predictably enters the draft as the top-ranked European skater, and he's expected to make the jump to the NHL immediately. Kakko is naturally gifted offensively, possesses a hard and accurate shot, and has showcased plenty of creativity to manufacture plays for his linemates.
Bowen Byram - Defenseman, Vancouver Giants
Byram is the consensus best defensive prospect in the draft and is projected by many to be a top-five pick. The blue-liner racked up more than a point per game in the regular season and led the WHL with 26 points in 22 playoff contests during his second full season with the Giants.
Kirby Dach - Center, Saskatoon Blades
Dach enters the draft as the third-ranked North American skater, and he has all the tools to become a prominent NHL center. He likely won't jump straight to the big leagues out of junior, but Dach immediately upgrades any team's prospect pool.
Alex Turcotte - Center, U.S. National Under 18 team
Turcotte is the fourth-ranked North American skater in the draft and projected to be taken in the top 10. The tenacious, two-way center plays the game at a high speed and possesses a strong hockey IQ. His elite skill set combined with a tireless work ethic and competitive edge help separate him from the pack.
The best impending free-agent defenseman is not hitting the market.
Multiple reports have Erik Karlsson staying in San Jose, with TSN's Pierre LeBrun tweeting that an eight-year contract extension worth north of $11 million per season is done.
As a result of Karlsson re-signing with San Jose, the Senators will receive a second-round pick in 2021 from the Sharks
The 2018-19 season was Karlsson's first in the Bay Area after a September trade from Ottawa, and the Swede finished with three goals and 45 points in 53 games. He added two goals and 16 points during San Jose's run to the conference finals.
Karlsson earned $6.5 million against the salary cap last season, the final year on his deal. He remains one of the league's top puck-moving defensemen and would have been in high demand in free agency, which opens July 1.
