"The facts here are so drastic and so apparent that the court should rehear it," Olson said.
In April a three-judge federal appeals court panel ruled 2-1 that Brady must serve a four-game suspension imposed by the NFL for the use of underinflated footballs at the AFC championship game in January 2015. The panel ruled that Goodell "properly exercised his broad discretion" in suspending Brady for his role in "Deflategate."
The panel overturned a ruling by a Manhattan judge, siding with the league in its battle against Brady and the NFL Players Association after an independent investigator found it was "more probable than not" Brady was "at least generally aware" of the scheme to deflate footballs.
Brady has repeatedly denied any involvement in the scandal.
En banc hearings — in which a case is heard by all of a court's judges rather than by a smaller panel of them — are rarely heard and often involve unusually complex cases, making it more likely those cases will end up being considered by the U.S. Supreme Court.
The SCOTUS has the discretion to reject an appeal. But it is inclined to take up cases in which the law is unsettled because of contrary rulings by lower courts, there are potential national implications and the issues may continue to be litigated by lower courts.
Sunday was the final day for the Patriots quarterback to file an appeal of his four-game suspension, after being granted an extension earlier this month.
According to his legal team, "Tom has been enjoying a low-key off-season, spending time with his family and going through his normal routine to prepare for the coming season, but for now has to sit back and await his fate for the season."