"We're still involved in our dialog, so there's no comment," Jones said as he was leaving a hotel in Chantilly, Va., where negotiations have been under way.
Asked if he was going to stay for more mediation sessions, Jones answered, "No, I'm going back to Dallas. That's all I'll say."
Late Tuesday, NFL Commissioner Roger Goodell and other league officials were meeting at the offices of the Federal Mediation and Conciliation Service in Washington, the Associated Press reported. The late-night meeting followed a four-hour negotiating session earlier in the day.
The current contract with the players' union expires at midnight EST on Thursday. Owners have threatened to lock out players if both sides don't strike a new deal by then.
Jones is a member of the owners' labor committee. His comments, following a three-hour meeting, shed little light on the status of the negotiations.
NFL spokesman Greg Aiello said both sides have agreed not to give any details of the talks.
"We'll get through this, and our commitment is to get an agreement, a fair agreement that is good for both sides as soon as possible without any disruption to the season," he said.
The Associated Press contributed to this report.