Morris, 28, is due to collect $1.2 million in the final season of the two-year, $3.5 million contract he signed last season.
Although the former Redskins Pro Bowler looked rejuvenated in training camp and in spot action behind Elliott early last season, he finished 2016 averaging a meager 3.5 yards on 69 carries.
Why are the Cowboys moving on from Morris? As an early-down power back with a limited skill set, he needs a steady diet of carries to justify his contract as well as his roster spot.
Coach Jason Garrett made it clear Thursday that he's not looking to reduce Elliott's workload on the heels of one of the most outstanding rookie seasons in NFL history.
Morris is a declining one-dimensional runner with an average of 3.67 yards on his last 271 carries. If Dallas manages to unload him, it will likely be for a conditional late-round draft pick.