The Jets suspended Byfuglien, who did not attend training camp, Sept. 21 with his full knowledge.
The 34-year-old has two years remaining on a five-year, $38 million contract (average annual value $7.6 million) signed Feb. 8, 2016. His salary would be $8 million this season and $6 million next season.
He had 31 points (four goals, 27 assists) in 42 games last season and eight points (two goals, six assists) in six Stanley Cup Playoff games. He missed 15 games from Dec. 31-Feb. 5 because of a lower-body injury and 19 from Feb. 16-March 28 because of a different lower-body injury.
Cheveldayoff said he spoke to Byfuglien a couple of days ago, but declined to get into any more specifics of the situation Monday.
"I basically have said the situation is status quo and it will remain status quo until you hear an announcement from the team or me at some point in time," he said.