US District Judge Richard M Berman has targeted September 4 as the latest date for his resolution, six days before Brady's New England Patriots open the season at home to the Pittsburgh Steelers.
Brady is facing a four-game ban after NFL commissioner Roger Goodell ruled that he conspired with two Patriots equipment employees to deflate balls prior to the start of January's AFC championship game – New England defeated the Indianapolis Colts 45-7 and went on to win the Super Bowl.
Berman announced his plans on Wednesday at the start of a hearing in which lawyers made verbal arguments that negotiations were continuing but have so far been unsuccessful.
Neither Brady nor Goodell were in court, but both have been told they must attend a hearing on August 31. Berman hinted he would still like both parties to come to some kind of “logical and rational” settlement.
ESPN's Adam Schefter reported Brady was open to accepting some kind of punishment, but only for his lack of cooperation with the inquiry, rather than the original case of ball-deflation.
Brady returned to practice with the Patriots on Wednesday in West Virginia, where the franchise was hosting joint sessions with the New Orleans Saints.