The running back has 187 carries for 913 yards (4.9 per rush), leading the NFL by nearly 300 yards rushing. Murray is on pace for 427 carries this season.
Cowboys executive vice president Stephen Jones reiterated to Adam Schein on Mad Dog Sports Radio on Thursday that the team would like to curtail the star running back's work.
"There's no doubt we'd like to get (Murray's workload) cut back," Jones said. "We want to do better in reducing his touches."
Murray's injury history -- and the diminishing returns on running backs who compile astronomical carries -- is a reason the Cowboys want to find another back to share the load.
However, Jones credited Jason Garrett for sticking with the ground game and cited the coach's growth as an important factor to the team's success in 2014.
"Anytime you have a great QB like (Tony) Romo, (you're) tempted to throw it around the yard," Jones said. "But Jason is maturing as a coach."