Murray said he did some running this week and has a target date for a return, but won't reveal it. He said Friday that missing his third straight game is "a little frustrating."
The Cowboys have rushed for 104 total yards in two games without Murray.
Compounding matters is the fact that Murray's replacement, Felix Jones, is nicked up with a bruised knee and nerve irritation in his neck. Jones, who is listed as probable, has been practicing and plans on facing the Falcons.
Cowboys executive vice president Stephen Jones said most players wouldn't take the field with the health problems that Felix Jones has.
As for Murray, there's a chance he could return against the Philadelphia Eagles on Nov. 11. Murray, who will play with a plate in his shoe when he does return, agreed with team officials by saying he doesn't want to rush his return, especially for the stretch run.
Also, wide receiver Dez Bryant is listed as questionable for Sunday's game as he has not practiced all week because of a hip injury.
Bryant, who suffered the injury on an apparent last-minute touchdown reception in the end zone Sunday against the New York Giants that was later overturned, fell to the ground Friday while trying to make a catch during a walkthrough drill. He was able to get up after a few seconds and walk back to the huddle.
Connor (neck stinger) had replaced Sean Lee, who was lost for the season two weeks ago with a foot injury.
Sims signed with the Cowboys on Oct. 24, but was able to learn enough of the sub package in just three practices to be effective last weekend against the New York Giants.
Wide receiver Kevin Ogletree is also questionable because of a hamstring injury that kept him out of practice for two days. Ogletree was limited in Friday's practice.
Information from ESPNDallas.com's Todd Archer was used in this report.