Jones said he didn't know why a conversation hasn't occurred and didn't have a timetable for when it may happen.
Bryant did speak with Cowboys coach Jason Garrett last week after the receiver was arrested and charged with a Class A misdemeanor for allegedly hitting his mother, Angela Bryant.
However, a source said Cowboys front-office officials met with Bryant's adviser, David Wells, for two days last week in Dallas.
Jones, who addressed the media at a news conference for the start of training camp, said the franchise takes Bryant's arrest seriously and touted its player-development program among the best in the league.
The Dallas district attorney's office hasn't determined if it will press charges against Bryant. Angela Bryant signed an affidavit of nonprosecution, meaning she doesn't want to proceed with charges.
"We take it very seriously," Jones said. "We're very supportive of Dez, his mother and his family. The issue is very serious, and I haven't spoken directly to Dez. But I do take it very seriously. We do not have all of the facts, all of the important details that are involved here. There are still some to evolve, but we all know it's no excuse. You guys are sitting there you didn't exactly have the silver spoon in your mouth either when you started out. I didn't either. But for a guy to have a hard road to (haul) and still have challenges is not an excuse, but it's a fact."
Jones said the organization has spoken with the NFL regarding Bryant's arrest. The league said it's reviewing the incident and wouldn't have any further comments regarding a possible suspension and/or fine.
"We're all well-aware of the conduct policy at the league level," Jones said. "And there again, that's premature because we've got to see the information and ultimately where it leads us. He did make the plane. He is here in camp, and that's all I want to say about it right now."