The Jets also announced that forward Mark Letestu will be out at least six months because of myocarditis, an inflammation of the heart muscle.
Cheveldayoff declined to discuss the team's relationship with Byfulgien other than to call it "complicated." He did not say whether Byfuglien might return to the team this season. The 34-year-old player was suspended without pay after failing to report to training camp in September, and there was talk that he may retire. Byfuglien had been granted a leave by the team for personal reasons.
The team said that the long-term health of the 34-year-old Letestu is not in question. The myocarditis is usually the result of a viral infection.
Letestu signed a one-year, $700,000 contract with Winnipeg this summer and had appeared in seven games with no points.
Cheveldayoff spoke Thursday in San Jose, California, a day after it was reported Byfuglien had surgery for a high ankle sprain last week in his native Minnesota.
Cheveldayoff wouldn't say whether there was a difference of opinion between the team and Byfuglien's camp on what kind of procedure was required stemming from the injury late last season.
Information from The Associated Press was used in this report.