Clowney was limited to conditioning work during Thursday's session, the team's first official practice of the week, and his official designation afterwards was that he did not participate in practice.
Defensive coordinator Romeo Crennel seemed to indicate that Clowney's status for Monday was contingent on his ability to take part in practice:
"Generally a guy needs to be on the practice field to play his best," Crennel said. "We're hoping to get him on the practice field so we can make a determination."
Clowney suffered a knee injury during the first half of Houston's Week 1 game against Washington; several days later he underwent surgery. According to the Texans' website, he has spent the last two weeks going through conditioning drills with team personnel.
Head coach Bill O'Brien said earlier this week that the chances of Clowney taking the field Monday night were about "50/50."
Monday will fall exactly six weeks after Clowney's surgery, from which team officials said he would need four to six weeks to recover.
On Thursday evening, O'Brien was more cautious, indicating that Clowney's status would be a game-time decision. He did say, however, that Clowney will be limited if he does play.