LSU coach Ed Orgeron said they'll make a decision on a daily basis this week about who will start, adding that he will not play Brennan if there's any risk of injury.
Should Brennan be unable to play, LSU would turn to freshman TJ Finley, who started in place of Brennan during Saturday's 52-24 win over South Carolina, throwing for 265 yards, two touchdowns and one interception. Finley also rushed for 24 yards and a score.
"If Myles is healthy, he's our first-team quarterback, but I'm not putting him in unless he's 100 percent," Orgeron said.
Whoever gets the nod at quarterback will be without starting sophomore left tackle Dare Rosenthal, who has been suspended indefinitely from the team.
Orgeron would not provide a reason for the suspension, saying, "I don't know when he's going to be back."
Rosenthal, who Orgeron has said has the potential to be an NFL player, left school in the spring for what Orgeron said at the time were "personal reasons." Rosenthal returned to compete in preseason camp, where he won the starting job.