Jones, the source said, finished the conversation believing that Parcells was never offended and that they will continue to share a good relationship.
Jones has not publicly commented on the story.
Parcells, now an executive with the Miami Dolphins, told The Record of New Jersey on Wednesday that he isn't worried.
"I know how he really feels about me," Parcells said, according to the newspaper.
He added that he and Jones have a good relationship. "I think he was just pulling some guy's leg. I'm not upset with it at all. He didn't mean it," Parcells said, according to The Record.
In the video, Jones appeared to be interacting with a football fan, unaware that someone was taping the conversation. At one point, Jones suggested that he hired Parcells to counter the perception that Jones was incapable of working with a head coach possessing a strong personality.
Reeves: There are no rules
"Bill's not worth a [expletive]," the video showed Jones saying. After some conversation with an unidentified man off-camera, the video continued with Jones saying, "... to get this [expletive] stadium, I need to bring his [butt] in."
Jones hired Parcells in 2003 following three straight 5-11 seasons. Although Parcells never won a playoff game in his four seasons with the Cowboys, he has been credited with rebuilding the roster that Wade Phillips used last season to end a streak of 13 consecutive seasons without a playoff victory.
Parcells also seemed to restore the franchise's reputation, which Jones used to help secure public funding for the $1.2 billion Cowboys Stadium.
The Cowboys made the playoffs in Parcells' first season with the team and again in 2006, when quarterback Tony Romo bobbled the snap on a potential game-winning field goal in the last minute of a playoff game at Seattle.
Sources: Receiver Miles Austin working out with Dallas Cowboys teammatesPires yet to decide
