Gregory's attorney, Daniel Moskowitz, who helped former Arizona Cardinals linebacker Daryl Washington gain reinstatement last year, declined comment.
Gregory, who has missed 30 of the past 32 games because of suspension, filed the reinstatement application within the past two weeks.
Last week, Cowboys executive vice president Stephen Jones said the proceeding was in the league's hands.
"We don't have anything to report differently, other than that I know he's wanting to move forward with the appeal," Jones said. "I don't really have anything new to report on that front other than that. I know he's done the application process, but I'm pretty sure he hasn't had the actual appeal. It's in the league's hands."
The NFL's substance-abuse policy states that once the reinstatement paperwork has been filed, "all individuals involved in the process will take steps to enable the commissioner to render a decision within 60 days of the receipt of the application."
There have been instances of the timeline being extended because not all of the steps have been completed in time.
Gregory fell to the Cowboys in the second round of the 2015 draft because of off-the-field issues during his time at Nebraska. Jerry Jones was willing to take the chance on Gregory and hoped a support system that helped other players through the years would help Gregory.
Gregory played in 12 games as a rookie in 2015, missing four with an ankle injury. He ended up in the NFL's substance-abuse program in 2016 and was initially suspended the first four games of that season. Another failed test led to an additional 10-game suspension, but he was able to return for the final two regular-season games and recorded the first — and so far only — sack of his career.
He was suspended for a year prior to the 2016 playoffs and has not been around the team since.
Gregory was eligible to file for reinstatement much earlier, but his advisors wanted to make sure all of the processes required for reinstatement had been met. Teammates Tyrone Crawford, Sean Lee and Jeff Heath wrote letters in support of Gregory to the NFL.
"It's best he's back in the locker room, [that] he's back around us," Crawford said earlier in the offseason. "I think it will be good for him and good for us."
On multiple occasions in the offseason, Jerry Jones said Gregory was doing well as he looked to rejoin the Cowboys.
"I have been proud of Randy during this offseason," Jerry Jones said May 9. "I'm very aware of how hard he's working to get back in the league and get back on the field."