Ware suffered a quad injury on Sunday Night Football in Week 6 against the Washington Redskins. He is listed as doubtful on the team's injury report after missing practice this week.
Meanwhile, Ware has never missed a game in his NFL career. He has a streak of 134 consecutive games played entering Sunday's contest.
Earlier in the week, Jerry Jones told ESPN the Cowboys would take a conservative approach with their star defensive end in Week 7. Still, Ware is known for recovering quickly, and that has been the case this week as well. Whether or not the Cowboys will be willing to let him rush back into action for a mid-season game remains to be seen.
Kyle Wilber is next up on Dallas' depth chart should Ware miss the game on Sunday.