The NFL Network and ESPN, meanwhile, were reporting that Romo had a herniated disc that could require surgery.
Romo, 33, aggravated his back injury during Sunday's 24-23 win against the Washington Redskins but continued to play on and found DeMarco Murray with a decisive 10-yard touchdown strike with just 68 seconds remaining.
"We haven't made that determination at all at this point," Cowboys head coach Jason Garrett said during a news conference when asked if Romo could be ruled out for the rest of the season.
Sunday's game between the (8-7) Cowboys and the (9-6) Eagles is a winner-take-all showdown that will decide the NFC East champion and a berth in the playoffs.
"He was able to play through it (on Sunday), and play very well at the end of that ball game. We evaluated it last night after the game and again this morning," Garrett said.
"There's going to be a series of different things we do for his treatment over the next few days and see how he responds to it. We'll see what his status is for Wednesday and this coming week."
Should Romo, a three-time Pro Bowl selection, be ruled out of Sunday's game against the Eagles, he is likely to be replaced by backup Kyle Orton, a former starter for Chicago and Denver.
Orton, 31, has completed three-of-five passes for 40 yards in two games for the Cowboys this season.
"We have Kyle Orton here for a reason," said Garrett. "But right now, we have a quarterback who is getting treatment for an injury. We want to get him involved in treatment as quickly as we can and we've started that process."
According to Cowboys owner Jerry Jones, Romo said he began feeling soreness during practice last week after his back tightened.
"We think it will be OK," Jones was quoted as saying by the Dallas Morning News. "It wasn't a contusion. It was a little tightening there.
"We will work on that all week ... he's kind of getting some special treatment for it. It didn't keep him from playing and won't keep him from playing."
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