Gregory is hoping to return for the 2018 season and to give the NFL enough time to have it approved before the start of training camp, tentatively set for July 24.
The NFL has 60 days to approve the application once the paperwork has been submitted.
This has been a painstaking and deliberate process for Gregory, who could have filed for reinstatement last month, a source said.
But he has been focused on doing everything necessary to have the best chance of success.
Per the NFL Network, Gregory has recently spent more than six weeks in intensive drug and alcohol rehab in addition to counseling.
That he has is able to file for reinstatement is a good sign that he has past muster with NFL doctors and has passed drug tests.
Per source, he met with NFL substance abuse program medical personnel over last weekend in Houston and “everything went well,” clearing the final hurdle for him to apply for reinstatement.
Gregory has the backing of several teammates who have written letters on his behalf and Cowboys owner Jerry Jones.
“I tried to give my two cents to the league and what I think is best for Randy,” defensive end Tyrone Crawford said last week. “I think it’s best he’s back in the locker room, he’s back around us. I think it will be good for him, and it’ll be good for us.”
Gregory hasn’t played since the regular-season finale in 2016. The league suspended Gregory on Jan. 6, 2017, for at least a year for repeated violations its substance abuse policy.
Gregory, who spent much of his time away in California, is hoping for another chance and the Cowboys are firmly behind him.
But they all know there are no guarantees with the NFL and this process.
“I have been proud of Randy during this off season,” Cowboys owner Jerry Jones said. “I’m very aware of how hard he’s working to get back in the league and get back on the field. We know his talent level. It’s concerning that he needs to be in a team environment and needs to be a part of the regime of preparing to actually compete, and so all of that will be a challenge for him, but very doable.
“I know him to be of the character and the kind of individual that is very capable of not only competing and overcoming the fact that he hadn’t played this past year. I think he’s capable of that. But I don’t want to be presumptuous in any way whether or not he’s going to qualify to be reinstated.”