Ware suffered a pulled quadriceps during the team's 31-16 win against the Washington Redskins. A source told ESPN Dallas that Ware is not likely to play this week but the team would not rule him out yet, either.
Ware said Monday he is doubtful to play against the Eagles. At 3-3, Dallas and Philadelphia share the lead in the NFC East.
"My body recovers really fast," Ware said. "I'm not going to be out that long."
Ware said he was feeling better.
"It wouldn't be 100 percent if I had to go out and play right now," Ware said. "There wouldn't be a point to this day. If I had to play, I wouldn't. I couldn't get off the ball."
Sources told ESPN earlier Monday that Ware could be sidelined three to four weeks.
Running back DeMarco Murray was injured against Washington as well and likely will be unable to play Sunday against Philadelphia, a source said. Murray suffered a sprained medial collateral ligament in his left knee.
Ware and Murray had MRIs on Monday.
After the game, Ware said he was fine and was walking without a limp. He has played in 134 straight games, making 133 starts. The only start he missed came Dec. 19, 2009, against the New Orleans Saints, when he had two sacks in a reserve role. Through six games this season, Ware has had to deal with a recurring stinger, a back strain, dehydration, getting poked in the eye and now the quadriceps strain.
Murray left Sunday's game after seven carries for 29 yards and a touchdown. Last year, Felix Jones played through a similar injury to both knees. Murray has yet to make it through a full season without getting injured. As a rookie he broke his ankle, and last year he missed six games with a sprained foot.
If Murray cannot play against the Eagles, the Cowboys would turn to rookie Joseph Randle, who had 11 carries for 17 yards and a touchdown against Washington. Lance Dunbar didn't play Sunday because of a hamstring strain, and Phillip Tanner had one carry for 2 yards.