Orgeron told reporters Wednesday that Brennan has not practiced this week and that if he can't play, freshman TJ Finley will get his second straight start.
Brennan has thrown 11 touchdown passes and three interceptions in three games this season.
"I don't believe he's going to play," Orgeron said of Brennan, "but things could change this week."
Finley, a former four-star prospect, threw for 265 yards, two touchdowns and one interception during a 52-24 win over South Carolina last Saturday. He also rushed for 24 yards and a score.
Orgeron said that offensive coordinator Steve Ensminger could expand the playbook now that Finley has gained the experience of his first career start.
"The thing I was most impressed with was his poise," Orgeron said of Finley. "He was so confident."
LSU, which went undefeated and won the national championship last season, has started this season 2-2.
Auburn came back late last Saturday to beat Ole Miss, improving to 3-2.