Tigers coach Ed Orgeron told reporters Monday that Brennan is dealing with a "significant" lower-body injury.
Orgeron added that Brennan, who got banged up during a loss to Missouri on Oct. 10, would not have been able to play against Florida last weekend had the game not been postponed due to COVID-19 concerns.
Brennan's 1,112 passing yards ranked 12th in the FBS prior to last weekend's games. He has thrown 11 touchdowns and three interceptions.
Should Brennan not be able to play against South Carolina, LSU could turn to either TJ Finley or Max Johnson to start at quarterback. Both are freshmen, but Orgeron expressed optimism in their abilities despite their inexperience, saying he thinks both players have NFL-level talent.
"They both had fantastic weeks," Orgeron said of Finley and Johnson. "Both of them are impressive."
He added, "Whoever has the best week is going to start."