Running back Lance Dunbar will be released by the Cowboys, a source said, and the goal is to bring him back to the practice squad.
The Cowboys need to keep four running backs around given the health status of Jones and Murray.
Jones has played 16 games only once in his career, and Murray missed the last three games of the 2011 season after he fractured his ankle.
But durability issues were raised in training camp when Tanner (hand) and Dunbar (hamstring) suffered injuries. It forced the Cowboys to play undrafted rookies Ed Wesley and Jamize Olawale and give Tavarris Williams snaps. Wesley was cut after being late to a walk-through meeting. Olawale, a fullback by trade, showed flashes that he can be a running back.
In the preseason finale Wednesday against Miami, Dunbar and Tanner each scored a touchdown and combined for 153 yards rushing.