Cowboys coach Jason Garrett said the team does not have a hard-and-fast rule that a player must practice in order to play.
The Cowboys (8-7) play the Philadelphia Eagles (9-6) on Sunday, with the winner clinching the NFC East title and a playoff spot.
If Romo, who has not attended meetings this week, cannot play against Philadelphia, Kyle Orton will start for Dallas.
"Certainly you want your quarterback to practice during the week," Garrett said prior to Thursday's practice. "Tony's played a lot of football for us, so you would give him more leeway than most.
"More than anything, it's a health issue, and we'll just see how he's feeling."
Romo received an epidural on Monday, which the Cowboys hope will alleviate some of the issues he is having from a herniated disk in his back. The Cowboys have not officially ruled Romo out of Sunday's game, but sources told ESPN's Adam Schefter and Chris Mortensen that he needs season-ending surgery.
Romo has played through pain countless times throughout his career, including playing multiple weeks with a cracked rib and punctured lung during the 2011 season. He managed to continue to play in last week's game against the Washington Redskins, directing a late game-winning drive with pain down his right leg.
"I think pain is probably the biggest issue, pain and how that relates to how you can function -- and there are a lot of different levels to that, walking around, moving around and all that," Garrett said. "You wake up in the morning, you evaluate it.
"Backs tend to kind of impact your whole body and how you can function in just day-to-day life. Hopefully he'll respond to some of the treatment and feel better as the week goes on."
Wide receiver Dez Bryant, who also is dealing with a back injury, practiced briefly Thursday before doing rehab work.
Bryant tweaked his back during Wednesday's workout, but the team does not believe the injury is serious.
ESPNDallas.com's Calvin Watkins contributed to this report.