Goodson made a brief appearance in court in Morristown on Wednesday. He and his attorney declined to comment afterward.
Goodson and a friend were arrested last month after they were found in a car stopped on Interstate 80. The men were charged with marijuana possession, possession of drug paraphernalia and weapons offenses. Police say they found a .45-caliber semi-automatic handgun and a hollow-point bullet in the vehicle.
The 25-year-old has pleaded not guilty and has taken part in some preseason practices with the Jets.
Assistant Morris County Prosecutor Peter Foy says no plea deal is on the table.