Witten was on the field for the start of practice Wednesday, which was a potentially good sign that he would be able to play Thursday despite a sprained left foot.
Media weren't allowed to watch the workout, so it was unclear how much he practiced or how he looked. Witten stayed in the training room and didn't speak with reporters afterward. He is listed as questionable.
"Jason's a tough guy, I know that," quarterback Tony Romo said following practice. "If he can go, he'll go, definitely."
Witten has the most catches and second-most yards receiving on the club. He's missed only one game in his career, back as a rookie in 2003, and only one game despite a broken jaw that required surgery.
"He's getting therapy, he's getting as many treatments as you can get," Phillips said. "We'll see how he feels."
Phillips has said this is the kind of injury that could get worse if he hasn't healed enough. But Witten's track record shows he's not likely to err on the side of caution, which means coaches have to think twice when he tries telling them he's fine.
Week 12 will have it all
"It's a little harder with guys like that because they want to play so bad that they feel like they can," Phillips said. "You have to rely on him to a certain extent, but also the medical people and what they have to say."
"If Jason's not out there there's a drop-off, no question," Romo said. "We're going to do the same things we do. We'll have to accomplish things. Everybody will have to pick things up if he can't go."
Romo was dismissive of questions about the back injury he sustained Sunday.
"We're improving each day," he said. "We'll be ready to go tomorrow, sure. ... I feel very strongly that we're going to be able to go out there and do what we normally do, so I'm excited. ... This short week, you have to watch a lot of tape and get extra treatment to make sure you're prepared for Thursday."
The Associated Press contributed to this report