Moore says no paperwork has been filed yet, but the process is underway and should ramp up in the next week to ten days.
Gregory was suspended indefinitely in February for violating the NFL’s substance abuse policy.
Gregory has been suspended four times as he’s battled substance abuse issues dating back to his time at Nebraska. He wound up missing the entire 2017 season while serving a suspension for another failed drug test before being conditionally reinstated in 2018.
The Cowboys signed Gregory to a one-year extension in April that will run through the 2020 season.
Gregory, 26, is a former second-round pick of the Cowboys back in 2015. He was entering the final year of his four-year, $3.814 million contract that includes $1.404 million guaranteed and stood to make a base salary of $955,217 for the 2019 season.
In 2018, Gregory appeared in 14 games for the Cowboys and recorded 25 tackles, six sacks, two forced fumbles and a recovery. Pro Football Focus rated him as the No. 75 edge rusher out of 103 qualifying players.