Brady and his attorney Jeffrey Kessler met with Goodell for 10 hours late last month to dispute the suspension. Brady was suspended by the league for his role in the use of deflated footballs in the AFC Championship Game win over Indianapolis.
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"I think we put in a very compelling case," Kessler said after the meeting in June.
The NFL Players Association had asked Goodell to recuse himself from hearing the appeal because he could not be impartial and might be called as a witness. But Goodell said it was his responsibility to oversee the hearing to protect the integrity of the league.
Based on the league-sanctioned Wells report, Brady was suspended and the Patriots were fined $1 million and docked a pair of draft picks.