Murray has missed the past six games with a sprained left foot, and despite being limited in practice all week, indications are he will play Sunday night against the Philadelphia Eagles.
"It looks like that, we'll see how well he responds (Friday)," Cowboys owner/general manager Jerry Jones said on his weekly radio show on KRLD-FM. "The key day was (Thursday), he came back better than (Wednesday), which was his first day out and usually that's a leveling off or setback day."
Murray, who practiced without incident on Friday afternoon, is listed as questionable on the official injury report.
With Murray out of the lineup, the Cowboys have used backup Felix Jones, who is playing with two sore knees.
Jones has averaged just 38.3 yards per game with Murray out of the lineup. Murray has rushed for 330 yards this season, five fewer than Jones, but produced a 131-yard game in the season opener against the New York Giants and a 93-yard performance at Baltimore.
"We'll see how he does in the next couple of days," Jerry Jones said. "It looks like we'll have him."
Safety Charlie Peprah will miss the next few games with a foot injury, according to a source.
Peprah's absence further depletes a secondary that already is without cornerback Orlando Scandrick, who had hand surgery and is out for at least the rest of the regular season.
Nose tackle Jay Ratliff, who hasn't participated in a full practice since Nov. 16 because of a groin injury, did some hard running during the early portions of Friday's practice. He's listed as doubtful.
"He is battling injuries," defensive coordinator Rob Ryan said. "He has all season. Believe me, if there is any way Jay can play, he will. I don't think that's going to be the case."
"You give him a chance," coach Jason Garrett said of Ratliff's possible return without practicing. "Let's give him a chance."
Information from ESPNDallas.com's Todd Archer contributed to this report.