The Cardinals will have first dibs on claiming Charlton, followed by the 49ers, Jets, Raiders and Bucs.
The Cowboys selected Charlton 28th overall in 2017, taking him two picks before the Steelers chose T.J. Watt. Charlton was a healthy scratch the first two games of the season.
He had four sacks in 27 career games.
Charlton was not at practice Wednesday, and the Cowboys had six players sit out with injuries. Receiver Tavon Austin (concussion), defensive lineman Tyrone Crawford (hip), receiver Michael Gallup (knee), linebacker Luke Gifford (ankle), defensive tackle Antwaun Woods (knee) and safety Xavier Woods (ankle) missed Wednesday’s work.