Redskins interim head coach Bill Callahan told reporters that Williams didn't pass his physical because of discomfort when he put on his helmet. In the off-season, the Pro Bowl offensive lineman underwent surgery to remove a growth on his head.
Callahan said Williams would have passed the physical if there was no helmet discomfort. He added that he wasn't sure if Williams would need a specialized helmet.
"I don't know all the specifics yet, but all I know is that the helmet, he wasn't comfortable," Callahan said. "A little discomfort in there. I'm sure it would be a part of the acclimation period of getting him back on the field. That was where it was going to begin.
"I'm going to leave that to the trainers and the doctors and the equipment manager, and see if they can all get together and formulate a plan of action and go forward from there."
The NFL gave the Redskins a two-week roster exemption for Williams, who previously said he would not play for the franchise again due to his dissatisfaction with the team's medical staff and their handling of the growth.
Williams reported before Tuesday's trade deadline, otherwise he would have needed the team to apply for his reinstatement with the commissioner's office. It remains unclear whether he will play another snap in Washington.
"I'm hopeful that he does," Callahan said. "I have a lot of respect for Trent. He's one of the more elite offensive linemen I ever had the privilege to coach. He has all the ingredients and has that makeup."
Veteran offensive tackle Donald Penn has started in place of Williams for the Redskins. Washington will play the Buffalo Bills on Sunday.