Gregory was suspended in January 2017 for violating the NFL's substance abuse policy.
Cowboys defensive end Randy Gregory will reportedly meet with NFL officials to discuss his reinstatement, according to ESPN's Todd Archer.
The meeting is set to take place in New York City and NFL commissioner Roger Goodell could potentially attend, reports Archer.
Gregory filed his reinstatement application during the past two weeks. According to the NFL's substance abuse policy, a decision will be made on Gregory's application within 60 days. Gregory's teammates Tyrone Crawford, Sean Lee and Jeff Heath wrote letters to the NFL on his behalf.
Cowboys owner Jerry Jones previously said that Gregory has been doing well.
"I have been proud of Randy during this offseason," Jones said on May 9. "I'm very aware of how hard he's working to get back in the league and get back on the field."
Gregory was suspended at least one year by the NFL in January 2017 for a missed drug test the previous November. It marks his third violation of the NFL's substance abuse policy.
The defensive end was suspended for the first four games of the 2016 season and then suspended for an additional ten games that year after failing another drug test.
The Cowboys selected Gregory in the second round of the 2015 NFL draft despite his first drug violation coming at the NFL combine. He has totaled one sack in 14 career games.