"We'll just have to see," Shurmur said. "We'll get him ready to go and if he can play, he will. If not, then we'll adjust."
Shurmur said Haden felt better and the injury is "something that can happen with a very harmless movement."
Haden was not in the locker room during the period it was open to the media for player interviews.
Haden, who was suspended four games earlier this season, got hurt during a drill in Wednesday's practice and sat out Thursday. The Browns (2-7) went 0-4 while Haden served his suspension for violating the NFL's policy on performance-enhancing substances.
Haden's injury comes just as the Browns defense was getting as healthy as it has been all season. Tackle Ahtyba Rubin practiced all week after missing three games with a calf injury and should be able to play alongside Phil Taylor for the first time this season. Taylor missed Cleveland's first seven games after undergoing surgery on a chest muscle he tore while lifting weights in May.
"I feel great," he said. "I can't wait to get back out there."
If Haden is ruled out against the Cowboys, Buster Skrine would likely start in his place opposite Sheldon Brown with rookie Trevin Wade moving into the nickel back position. Special teams star Johnson Bademosi could also get time at cornerback.
Shurmur is confident the Browns will be able to compete -- with or without Haden.
Copyright 2012 by The Associated Press