The meeting was first reported by The Dallas Morning News.
Jones has not been allowed to visit the Cowboys' Valley Ranch facility or take part in any organized team activities, but he is hopeful the league will allow him to do so this week, according to the report.
But sources said if the NFL doesn't allow Jones to practice with the team, the Cowboys are hoping the league will allow him to undergo counseling at the facility and interact with his new teammates, the newspaper reported.
Pacman Jones has been on indefinite suspension since March of last year -- missing the entire 2007 season -- after several run-ins with the law. Last week, he cleared up a $20,000 gambling debt at a Las Vegas casino after the local district attorney threatened to bring felony charges against him.
Cowboys owner Jerry Jones told ESPN's Ed Werder that both he and the league office were aware of Pacman Jones' overdue gambling debt before the meeting between Goodell and Pacman. Jerry Jones contends the perception that disclosure could affect reinstatement is wrong.
Jerry Jones says he has no time frame for any league decision and would not describe himself as optimistic. He also insists he's staying out of it.
"I don't think it's my place to get in here and call them up and say, 'What'd he say? What'd he do? What do you think?'" Jones said.
The owner stressed the Cowboys are following orders, having no official interaction with Pacman Jones, not even giving him a playbook. But they are keeping tabs.
"Adam is really working hard and zeroing in on all the things that it takes to be an NFL football player," Jerry Jones said. "Relatively speaking he's in good shape -- certainly not ready to play a ballgame but nobody else out here is either. The main thing is he's working hard. I feel that he certainly will take advantage of this opportunity to play with the Cowboys. I think it's going to work."
Providing the commissioner gives him that chance, Jones quickly added.
Pacman still can't set foot on team property, much less join his new teammates for organized team activities being held Tuesdays, Wednesdays and Thursdays. Goodell could give permission for either of those without fully welcoming him back to the league -- sort of like he did with Tank Johnson last year. Goodell let Johnson practice about a month after being signed, three weeks before his suspension ended.
The status of the suspended cornerback remains the main topic of interest surrounding the Cowboys, especially with each nugget of progress in his bid to get reinstated.
Ready and waiting, Jones already has moved to Dallas and is hanging out with his new teammates. He attended Jason Witten's charity bowling event, worked out with some Cowboys at SMU and recently was at a party hosted by Deion Sanders.
"I teased him," receiver Terrell Owens said. "We went inside and were playing around on the basketball court, and I asked him if he was ready to play. He said, 'Yeah, but we're not going to no strip clubs this year either.' Everybody is going to welcome him. I think he's going to try to keep his nose clean, and I think that's going to be best for him anyway in order for him to stay in the league and obviously to stay on this team."
Johnson plans to make sure of it.
Casual acquaintances as NFL players, they became linked as guys who endured Goodell's wrath. Now their Cowboys connection has turned them into kindred spirits.
The team's department that works with troubled players hooked them up as sort of a mentorship. Nate Newton, Michael Irvin and others helped Johnson, and now he's reaching out to Jones.
"I speak to him on the phone often," Johnson said. "His head is in the right place. He's eager to get out here with his teammates. He's eager to get acclimated to our system. He understands the position he's in, and he's ready to prove everyone wrong. It's tough when you've been through as much as he has in such a short amount of time. He knows it's his last straw, so he's going to take extreme caution to everything he does."
Johnson's best advice?
"You got to make sure your good decisions outweigh your bad ones," Johnson said. "I told him, 'I will be your right hand. Whatever you need, I will be there for you.'"
Speaking from experience, Johnson said it's important to know the Cowboys have a support system in place.
"I felt like my back was against the wall and the world was against me and there was no one in my corner. I think for him to feel that there's someone in his corner who is supporting him, who cares about him, who wants to see him succeed -- sometimes that's all you need," Johnson said.
"Now that I've gotten a chance to know him on a personal level, I think he's definitely matured a lot through this process. I think he's figured a lot of things out. I think the maturation process for some is slower than others. Mine was a little slower, but now it's gotten to a point where I can handle myself. And I think Pacman is at that same level."
Johnson said he still speaks regularly with Goodell. However, he wouldn't say whether he's put in a good word for Pacman.
"He's a good guy, a fair guy, and he's going to do what's best for this league," Johnson said of the commissioner.
Jones pleaded no contest Dec. 6 to conspiracy to commit disorderly conduct in a deal that reduced two felony charges of coercion stemming from a February 2007 Las Vegas strip club shooting that left a bouncer paralyzed. The coercion charges each carried a possible sentence of one to six years in prison.
In return, Jones agreed to tell police what he knew about the gunman. Jones never acknowledged any role in the shooting.
The alleged gunman, Arvin Kenti Edwards, was arrested in April after Jones picked him from a police lineup, and remains jailed in Seattle pending an extradition hearing.
Information from ESPN's Ed Werder and The Associated Press was used in this report.