Garrett needs to hire a running backs coach after the team elected not to retain Skip Peete, who took over the same position for the Chicago Bears.
The Cowboys have expressed interest in several coaches, including Sam Gash, Gary Brown and Tim Spencer.
Gash was the Detroit Lions' running backs coach from 2007-12 and played for five NFL teams.
Brown was in charge of the Cleveland Browns' running backs from 2009-12. Brown played for three NFL teams.
Spencer, who used to play with the San Diego Chargers, led the Chicago Bears running backs since 2004 until he was let go after the 2012 season.
Cowboys owner/general manager Jerry Jones said he didn't expect to finalize the coaching staff with Garrett while they were in Mobile, site of the Senior Bowl. Defensive coordinator Monte Kiffin said the defensive coaching staff is complete. Kiffin added just one coach, Rod Marinelli, to coach the defensive line.