Romo suffered a fractured rib in last Sunday's 27-24 overtime win at San Francisco. He was also diagnosed with pneumothorax, otherwise termed a collapsed lung.
"There's nothing that's been cleared 100 percent either way," Romo said. "We've been cleared with the pneumothorax, dealing with the lung. That part of it was the first step."
Romo said that if he's cleared, he would be on the field for Dallas' home opener and fight through the pain.
"If it has to deal with just the pain, that's part of playing as a quarterback in the NFL," he said.
Romo, who missed more than half of the 2010 season due to a broken left clavicle, suffered his latest injury in the first quarter against the 49ers. He missed nearly the entire third quarter while getting treatment, but came back and rallied the team to overtime, connecting with Jesse Holley on a 77- yard pass play to set up Dan Bailey's game-winning field goal.
Romo went 20-of-33 for 345 yards and two touchdowns.
Dockery suffered a fractured tibia and sprained MCL in the third quarter of last Sunday's victory.