Gregory will submit his application for NFL reinstatement on Thursday, NFL Network Insider Ian Rapoport reported on Wednesday, citing a source informed of the situation.
The 25-year-old Gregory hasn't played since the 2016 regular-season finale. He sat out the entire 2017 campaign after being suspended for at least one year for violating the NFL's policy for substance abuse.
Gregory must follow a series of steps in the reinstatement process, providing thorough information on his treatment and any incidents that occurred during the period of his suspension.
Following the receipt of Gregory's application by NFL commissioner Roger Goodell, the league's medical director and medical advisor will interview Gregory within 45 days and subsequently file a recommendation to Goodell.
A second-round pick in the 2015 NFL Draft out of Nebraska, Gregory has played in only two games since his rookie season. He has recorded only one sack in 14 career games with the Cowboys.
Gregory was suspended without pay for at least one year in January 2017. It was his third suspension in one year. He then tested positive for marijuana in April 2017, marking the seventh time he tested positive for a banned substance.
The 6-foot-5, 255-pound Gregory was suspended for the first four games of the 2016 season and had an additional 10-game ban imposed on him in September. He returned to play in the final two weeks of the regular season before earning his suspension of at least a year.
Gregory also failed a drug test for marijuana at the 2015 NFL Combine.