Goodson, who was released by the Jets last week with the designation "left squad," could be arrested if he fails to appear in court for a July 24 hearing before Judge Mary G. Whipple.
Goodson's attorney was in court Thursday morning, as was Goodson's co-defendant, Garant Evans.
According to the Newark Star-Ledger, Goodson's acting attorney, Alfred Gellene, said that Goodson was unable to secure a flight from Texas, where he has been since the end of the Jets' season. The reason for the difficulty was "financial issues" Gellene said, according to the report.
Anthony Fusco, Goodson's attorney of record, had no further comment.
Goodson was arrested in May 2013 after being found unresponsive in a vehicle found stopped in the left lane of Route 80. Police found an unregistered gun with a hollow-point bullet in the car, and in November both Goodson and Evans were indicted on possession charges.
New Jersey has some of the strictest weapons laws in the country, and Goodson faces up to 10 years in prison if found guilty.
The Jets signed Goodson to a three-year, $6.9 million contract in March 2013, but he played in only two games before he was released.
The Jets had trouble this offseason getting in touch with Goodson, who did not check in with coach Rex Ryan or doctors despite rehabbing an MCL and ACL tear. When he didn't show up for the team's mandatory minicamp on June 17, the team cut him.
Jets general manager John Idzik was asked if he took too much of a risk on Goodson, who had issues before coming to the Jets.
"We're in the human business," Idzik said after releasing Goodson. "We certainly do our due diligence. You can do as much research as you can, but you're really not going to know for sure until you get that individual in your organization and try to acclimate them to what you want to do."