Kearse has been sidelined with an abdominal injury and recently underwent a medical procedure, the New York Daily News reported Friday, citing sources.
Entering his seventh NFL season overall and second with New York, Kearse missed the final two preseason games because of the injury.
Jets coach Todd Bowles was vague on Kearse's condition, telling the newspaper recently that he was "getting better every day."
As far a potential timetable for Kearse's return, Bowles labeled him "day-to-day, week-to-week."
The 28-year-old Kearse appeared in 16 games, making 14 starts, for New York last season, hauling in a career-best 65 receptions to go with five touchdowns.
"He does all the little things," Bowles told the newspaper." He does all the things right and he's a gamer. He shows up on Sunday -- every Sunday -- and I think he's been a good guy for the young guys, young receivers to follow after from a work ethic standpoint."
That unit was thinned out Friday when wide receiver Charles Johnson was among seven players reportedly cut by New York.