Citing ESPN's John Clayton, The New York Post on Monday reported that the Jets are not likely to sign the former Giants star.
"The Bears are pretty much all but ruled out the possibility of bringing (Burress) in and the Jets are almost in the same boat," Clayton said. "Nobody is going to bring him in before the start of training camp, it looks like."
Over the past few weeks, the Jets publicly voiced their interest in Burress, most likely because he would have given rookie quarterback Mark Sanchez a proven target to throw toward.
Burress, who shot himself in the thigh November 29 in a Manhattan nightclub, was charged with criminal possession of a weapon and faces up to three and a half years in prison.
Burress made an appearance in court early last week, where Judge Felicia Mennin adjourned the case until Sept. 23, enabling the former Super Bowl hero to continue negotiations with several NFL teams.
The 31-year-old receiver recorded 35 catches, 454 yards and four touchdowns in 10 games last season.