The case moved to federal court when the NFL asked a judge to validate its upholding of a four-game suspension. The players association, representing Brady, appealed the suspension in court after the NFL's filing.
U.S. District Judge Richard M. Berman hasn't ruled in the case, which centers the suspension imposed on Brady for allegedly knowing the Patriots used footballs inflated below league-mandated levels in the AFC championship game.
Another hearing is scheduled for August 19. Lawyers will file more briefs by Friday.
The judge met privately with Goodell and his lawyers and then with Brady and his legal team, reported CNN's Rachel Nichols.
During a public session, the judge questioned lawyers, but not Brady or Goodell.
At one point, the judge asked NFL lawyer Dan Nash if there was any direct evidence showing Brady knew footballs were underinflated.
Nash said that there is no text message specifically showing that Brady instructed someone to put a needle in a football.
Berman also asked questions concerning Ted Wells' dual role as an investigator for the NFL and an attorney hired by the league.
Berman asked lawyers for the NFL Players Association why Brady had broken a cell phone that was central to the investigation.
So far, neither side had budged, at least publicly.
Goodell stands by his decision to suspend Brady four games for allegedly knowing about the inflation levels.
Berman is "known among his colleagues as a settlement judge" and is urging both sides to settle the case, Nichols said.
Another important date is September 10. That's when the Patriots regular season starts against the Pittsburgh Steelers.
Crowds outside the Manhattan courthouse on Wednesday cheered when Brady entered, with one man shouting, "Don't settle, Tom." Brady is one of the best-known and richest athletes in the United States, with three Super Bowl victories on his resume.
Goodell, commissioner since 2006, was greeted with boos.
Also on Wednesday, the full transcript of a July 23 appeals hearing was unsealed.
In the transcript, Brady says that after the scandal broke he talked to the ball attendant accused of deflating the footballs and the attendant said he didn't do anything improper.
Deflategate erupted after the Patriots won the January 19 AFC championship game over the Indianapolis Colts.
Wells, hired to investigate, said Brady "was generally aware" the team had used underinflated footballs, which are easier to grip and provide a competitive advantage for some players, according to some experts.
Brady, who led the team to a Super Bowl victory over Seattle, denied involvement.
Goodell suspended Brady the first four games of the 2015 season. Brady appealed and on July 28 Goodell upheld his own decision, further criticizing Brady by saying he'd destroyed a cell phone containing text messages that were central to the investigation.
Brady said he'd cooperated with investigators and wasn't trying to hide anything when he broke the phone.
The NFL's original investigation report, released last May, said the likely perpetrators were equipment assistant John Jastremski and the man who carried the balls from the officials' locker room to the field, Jim McNally.
But Wells said "it is more probable than not" that Brady was "at least generally aware of the inappropriate activities."
The Patriots were punished, too. The team was fined $1 million and will forfeit its first-round selection in the 2016 NFL Draft and its fourth-round pick in the 2017 draft.
Team owner Robert Kraft said he regretted cooperating with the Wells investigation. "I was wrong to put my faith in the league," he said.