A termination would end the defenseman's suspension and nullify his grievance against the team. It would also serve as a significant step on Byfuglien's path to unrestricted free agency.
Neither side can independently terminate the final two years of the deal - both sides need to sign off on it - and Byfuglien would then have to clear waivers before becoming a UFA, according to The Athletic's Ken Wiebe.
The gargantuan blue-liner has missed the entire 2019-20 season after undergoing ankle surgery in October. The Jets suspended him in September after he didn't report to training camp, and the NHLPA filed a grievance on his behalf in November.
Byfuglien hasn't resumed skating since the ankle procedure. The 34-year-old's camp has argued the injury was a hockey-related ailment sustained during the 2018-19 season and that it never fully healed, but the team deemed him healthy after he passed his end-of-season physical in April.
The veteran rearguard's ban was procedural in nature and he hasn't been paid since being suspended. Byfuglien's contract originally carried a $7.6-million cap hit for both this season and the next campaign, along with salaries of $8 million in 2019-20 and $6 million in 2020-21.
Terminating the deal would bring closure to the dispute while providing the Jets with cap flexibility ahead of the Feb. 24 trade deadline.