The 5th U.S. Circuit Court of Appeals in New Orleans heard oral arguments from the NFL and NFLPA on a stay in the Ezekiel Elliott suspension case and issued no decision on Monday.

The NFL will file a response brief by Tuesday morning. The court said it will rule quickly once that brief is filed.

The NFL is seeking a stay of the injunction that is keeping the Dallas Cowboys running back on the field.

At issue is the lawsuit that the NFLPA filed which overturned Elliott's suspension. The union argues the lawsuit was correctly pursued because the arbitration proceedings were complete, except for the final ruling, which went against Elliott.

NFL attorney Pratik Shah said the arbitration proceedings, called for in the league's collective bargaining agreement, had not been exhausted, so U.S. District Judge Amos Mazzant lacked jurisdiction when he blocked the suspension.

Questioned closely by the appeals panel, players' association attorney Jeffrey Kessler insisted that the suit was properly before Mazzant, with all but the ruling pending.

"You don't have to wait to be run over," he told the judges.

Also at issue was whether the NFL would be "irreparably harmed" by a court-imposed delay in its disciplinary decision, or whether Elliott would suffer irreparable harm if forced to immediately serve the suspension.

When the court issues its ruling, there are three potential outcomes:

The Court of Appeals could rule that the district court lacked authority to hear the case and rule to vacate the injunction and dismiss the lawsuit, in which Elliott's six-game suspension would take effect immediately, although Elliott would likely file a temporary restraining order.

The court could vacate the injunction based on the merits of the case, believing the district court overreached when reviewing the decision, particularly given how the courts ruled in favor of the league in the Tom Brady and Adrian Peterson cases.

The court could deny the stay, which likely means Elliott would be able to play for the full season, and the legal battle to play out for the 2018 season.

Elliott was not in attendance on Monday. He attended the injunction hearing in Sherman, Texas, before the season started.

Until the court decides that District Court Judge Amos Mazzant had the right to hear Elliott's appeal or whether to dismiss lawsuit altogether, the running back will be eligible to play.

The Cowboys are hopeful Elliott will be able to play Sunday against the Green Bay Packers but will be ready to adjust if necessary. Through the first month of the season, the Cowboys have not spent time tailoring their game plans for RB Alfred Morris or RB Darren McFadden in case Elliott had not been allowed to play during the court process.

"We've been focused on constructing game plans as if Zeke were our running back, and we feel like that the skill set of the guys behind him allow them to go in and just go play," coach Jason Garrett said. "So that really hasn't been something we've spent a lot of time doing."

Elliott had the sixth two-touchdown game of his career Sunday, rushing for 85 yards on 21 carries, and caught four passes for 54 yards and a touchdown in the Cowboys' 35-30 loss to the Rams.

ESPN's Todd Archer and The Associated Press contributed to this report.