The N.B.A. players union is asking an arbitrator to clarify certain free-agent rights in a case that could immeasurably benefit the Knicks this summer, according to several people involved in the process.

The case concerns what are known as Bird rights, which allow a player to re-sign with his team without regard to the salary cap. The league contends those rights are lost when a player changes teams through waivers. The union is challenging that interpretation.

If the union prevails, the Knicks would be able to re-sign both Jeremy Lin and Steve Novak, their top free agents, despite cap constraints. They would also retain a $5 million salary slot — known as the midlevel exception — for use on another player, possibly J. R. Smith, who can opt out of his deal.

But if the union’s challenge fails, the Knicks will probably lose Novak and possibly Smith when free agency opens in July. And they will have little ability to sign a significant free agent like point guard Steve Nash once they re-sign Lin.