All signs, however, point to the Texans starting rookie Deshaun Watson. He took every snap with the first-team offense during the short portion of practice open to the media on Tuesday.
Watson tweaked his ankle in Sunday's game and was on the Texans' injury report on Monday, but was listed as a full participant Tuesday.
However, the team continues to monitor his progress.
"The health of any player is the first determinant in whether they play or not," O'Brien said Tuesday.
Watson relieved Tom Savage in the second half of Sunday's 29-7 loss to the Jacksonville Jaguars after Savage and the offense struggled to move the ball. Savage was 7-of-13 for 62 yards and was sacked six times. Watson did not fare much better, going 12-of-23 for 102 yards with a touchdown and an interception.
Watson did, though, lead the Texans down the field on his first NFL drive, throwing a 4-yard scoring pass to DeAndre Hopkins for the Texans' only points of their opener.
Savage has been the Texans' starting quarterback since they traded Brock Osweiler in March, even after Houston moved up in the first round to draft Watson. O'Brien said on Monday that although Savage took the majority of the snaps with the starting offense during training camp, Watson took a large portion, as well.
Along with Watson, the Texans had 20 other players on the injury report, including five in the concussion protocol. O'Brien said those five players are unlikely to play Thursday because of the short week, but if any of them could be cleared from the protocol in time, it would be tight end Ryan Griffin and wide receiver Bruce Ellington.
On Tuesday, the Texans put starting tight end C.J. Fiedorowicz on injured reserve to activate wide receiver Jaelen Strong from the reserve/suspension list. Fiedorowicz left Sunday's game in the concussion protocol; he previously suffered a concussion during the preseason.
The Texans visit the Bengals on Thursday night, with kickoff set for 8:25 p.m. ET.
Cincinnati coach Marvin Lewis said he anticipates Watson starting.
"We're kind of planning on it being Deshaun because if they made the change like they did at halftime, I would imagine it would be him coming forward here, at least this week," he said.