The 33-year-old defenseman has missed 12 games because of a lower-body injury sustained in a 3-1 loss to the Minnesota Wild on Dec. 29.
"We are now in day to day," Jets coach Paul Maurice said prior to Winnipeg's game against the Columbus Blue Jackets (8 p.m. ET; TSN3, FS-O, ESPN+, NHL.TV). "So if he comes back tomorrow and he feels good, we'll take him out with the coaches and give him a pretty good tug on the ice. And if he feels better the next day we'll get him back with the team and start getting into some tight turns and things like that. It's almost like a version of a concussion. You just keep incrementally increasing the work load."
Byfuglien, who has 29 points (four goals, 25 assists) in 32 games this season, was on the ice prior to the morning skate Thursday.
"He has to get handed off to the coaches here, sometime maybe tomorrow, maybe the next day, [and we start pushing him harder]," Maurice said.
Maurice said forward Nikolaj Ehlers is at least a week away from a return.
Ehlers has missed the past 10 games since sustaining an upper-body injury on a hit from Pittsburgh Penguins forward Sidney Crosby in a 4-0 loss Jan. 4. He has 27 points (15 goals, 12 assists) in 40 games this season.
"Nik is more defined, he's not getting a green light to get back on the ice until a certain number of days on his injury," Maurice said. "Once he passes that, we will get him in there. His window is just opening up. Feb. 4 would be the start, the very earliest he would join us, but he's not getting into a game for another week at least."