Goodson was arrested Friday morning during a traffic stop in New Jersey after the car he was a passenger in was stopped in the left-center lane of Route 80.
Goodson was charged with unlawful possession of a handgun, possession of a loaded handgun, possession of hollow-point ammunition, possession of marijuana and drug paraphernalia. Goodson was released on $50,000 bail after spending more than 12 hours in jail.
The team is currently going through organized team activities and those are voluntary. Goodson did not participate or even see the OTA's, according to the report.
Jets owner Woody Johnson said the team still is investigating the matter.
"We're at a point of investigating the facts," Johnson said to USA Today. "[General manager] John Idzik met with him this morning, he'll meet with the coaches today. We'll try to get the story on what the facts are and go from there. We're trying to win games and do the right thing. Truth, justice and the American way. We live by it, we really do."