The N.A.A., the NCAA and the NFL are all expected to argue that a federal court must rule soon on whether the players should be paid, and that the state should pay them, even if they have not been named in court documents as defendants.
It would be a first for the court, which is considering a lawsuit by the University of North Carolina, alleging that the school violated the antitrust laws when it hired former NFL quarterback Josh Freeman in 2013 to play for the Tar Heels.
A decision is expected within the next two weeks, with arguments expected on Thursday and Friday.
If the court rules against the NCAA, it would be the first time the court has ever ruled on whether athletes have a constitutional right to receive compensation for work they did while on the job.
The court has repeatedly ruled that the antitrust act does not protect the NFL and N.H.L. from antitrust suits by other sports.
If a trial were to take place, the plaintiffs would be represented by the law firm of Davis Polk & Wardwell, which has represented the N.