Jones confirmed Gregory's plans with the hope that the 25-year-old can play in the upcoming season, per David Helman of the team's website. Gregory became eligible to apply for reinstatement in November but has yet to go through the process.
Gregory missed the entire 2017 season after being suspended for at least one year for violating the NFL's policy for substance abuse.
A second-round pick in the 2015 NFL Draft out of Nebraska, Gregory has played in just two games since his rookie season. He has recorded just one sack in 14 career games with the Cowboys.
Gregory was suspended without pay for at least a 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.
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.
The 6-foot-5, 255-pound Gregory also failed a drug test for marijuana at the 2015 NFL Combine.