The NFL has not announced more than a four-game suspension for Gregory, and the league still considers his potential "4-plus-10" suspension to be pending, according to the source.
When final roster cuts were made Saturday by NFL teams, there was a mention next to Gregory's name on the Cowboys' roster of a four-game suspension, but that was in reference to his violation announced in February, not the additional violation reported in July, which the NFL has not made any announcement about.
It is unclear whether Gregory violated the substance abuse policy by failing or missing a test, but he is facing the possibility of having the suspension extended.
A source told ESPN on Sunday that agent Deryk Gilmore filed an appeal and sent the league documentation to support the contention that Gregory did not commit a violation that should add to his previously announced suspension. There has not been a hearing on the matter, the source said.
The Cowboys placed Gregory on the reserve/did not report list at the start of training camp but have remained supportive and have a locker for him at The Star, their new practice facility.
At the 2015 NFL scouting combine, Gregory tested positive for marijuana, which put him in the league's drug program. Considered a first-round prospect out of Nebraska, he fell to the second round, where the Cowboys selected him with the 60th overall pick.
The Cowboys and Gregory agreed that he would have a personal handler with him during the season to help him cope with issues related to anxiety.
Gregory played in 12 games as a rookie and did not record a sack. He suffered a high-ankle sprain in the season opener against the New York Giants and missed the next four games. Cowboys coaches credited him with 11 tackles and 16 quarterback pressures to go along with one tackle for loss.
The source said Gregory continues to receive inpatient treatment at a drug rehabilitation facility.
The reduction in the suspension was first reported by the Fort Worth Star-Telegram, and two sources initially told ESPN the same information.