Palmer didn't participate in practice Monday and is expected to sit out Thursday night against the St. Louis Rams. That would leave only one more preseason game -- against Indianapolis on Sept. 3 -- but it's unclear whether he'll be able to play in that game, either.
Instead of practicing, Palmer got treatment on the ankle Monday. He also played catch to try to keep his arm in shape.
"I can throw, but not drop back right now," he said. "I'm trying to keep my arm in shape, basically. I'll take it day-to-day."
Palmer is the Bengals' biggest concern with less than three weeks left before the opener on Sept. 13 against Denver at Paul Brown Stadium. He missed a dozen games last season because of a torn ligament and tendon in his passing elbow.
The elbow has healed on its own, allowing Palmer to participate fully in offseason workouts, minicamp and the start of training camp. He suffered a moderate high-ankle sprain when he was hit while throwing a pass during the preseason opener at New Orleans on Aug. 14. He sat out a 7-6 win at New England last week.
Palmer wore an ankle brace on Monday as he walked through the locker room on his way to a meeting. He said the ankle is getting a little better each day, and he would have likely played this week if it was a regular-season game.
"We're being cautious with where we're at," Palmer said. "I've had great work during training camp, but the training staff has decided it's best to have me ready for the opener. I would like to play in every game, I would like to play three quarters in every game. Nobody does that, and obviously I haven't been able to do that."
With Palmer injured for most of last season, the Bengals' offense finished last in the league. They've moved the ball much better in the first two preseason games, but failed to score because of mistakes. The Bengals have scored two touchdowns in the two games, both on passes from O'Sullivan to Chris Henry.
Coach Marvin Lewis declined to say whether he might play Palmer in the final preseason game to make sure he's sharp for the opener.
"I can't worry about Carson's sharpness right now," Lewis said. "If Carson's in there and playing, then we're fine and we'll go forward. We'll cross that bridge next week."