"There's a possibility Tony's going to hold," coach Jason Garrett said.
The Cowboys have tentative plans to work out some punters once they get a feel for the health of Jones, who suffered a sprained knee Sept. 23 against Tampa Bay, when he nearly had a punt blocked, and Moorman, who strained his groin before Wednesday's practice.
Jones has practiced a bit the past few days and has been getting treatment.
"The concern is he's not completely healthy so you just have to see where his knee is as this week progresses," Garrett said, "(and) see if he's able to punt and function and the way we need him to function."
Romo held for kicker Dan Bailey last year as Mat McBriar worked through a nerve condition. Romo has had the job at different times since his famous bobble in the 2006 wild-card playoff game at Seattle.
Garrett said backup quarterback Kyle Orton would be another candidate if Jones and Moorman cannot play, or if a possible new punter does not have holding experience.
Jones has averaged 46.4 yards per punt with a 40.7-yard net average in three games. Five of his 11 punts have been downed inside the 20. Moorman averaged 37 yards per punt against Chicago with a 34.3-yard net average and had two punts downed inside the 20. Cowboys opponents are averaging just 5 yards per punt return this season.
Bailey punted twice last year at Philadelphia, with a 39.5-yard average, after McBriar was forced out of the game.
"He's a guy that's been able to do that for us in the past," Garrett said. "He's obviously not a punter. He's a kickoff and field goal guy, but he has some versatility. He's a very good athlete and he's a very poised guy, so if we need him to do that in a given situation, although not ideal, he's capable of doing that."