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U.S. District Judge Richard Berman in Manhattan in a court order on Tuesday requested that both sides "engage in further good faith settlement efforts" before a court hearing on Wednesday.
The New England Patriots quarterback was suspended for four games over his alleged role in a scheme to deflate footballs in the Patriots' 45-7 victory over the Indianapolis Colts in a January playoff game. NFL Commissioner Roger Goodell confirmed Brady's suspension on July 28.
The judge, who has been pushing for a settlement, said he would meet privately with the parties on Wednesday for an update on their talks before a previously scheduled hearing.
It's unclear if a deal can be reached. NFL spokesman Brian McCarthy on Tuesday said in an email to Reuters the league "has been, and will continue to comply with the judge's order."
George Atallah, a National Football Players Association spokesman, declined to discuss the settlement talks.
Ted Wells, an attorney hired by the NFL to investigate how the footballs were inflated below league standards, placed the blame on two Patriots employees but said that Brady was "at least generally aware" of the plan.
An under-inflated football is easier to grip for a quarterback, especially in raw outdoor conditions like January's American Football Conference title game outside of Boston.
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The union claims Goodell was not an impartial arbiter because he had praised Wells' work before the appeal, while the league has argued that Goodell was authorized to conduct the hearing under the terms of its labor agreement.
The NFL and the union have asked Berman to decide whether to uphold the suspension by Sept. 4, six days before New England's 16-game season begins in a nationally televised game against the Pittsburgh Steelers.
If the injunction is not granted, Brady would not return until Oct. 11 when the Patriots visit the Colts.
(Editing by Matthew Lewis and Alan Crosby)