Brennan started the first three games in 2020 before suffering a torn abdominal muscle at Missouri that ended his season. He was set to compete with Max Johnson for the starting job this summer but broke his left (non-throwing) arm during a fishing trip that required surgery.
Johnson, a sophomore who replaced Brennan down the stretch last season, has started all eight of LSU's games this season.
Brennan, who backed up Heisman Trophy winner Joe Burrow in 2019, is in his fifth year with the LSU program. ESPN rated the Long Beach, Mississippi, native as the No. 4 pocket passer and No. 96 overall player in the 2017 recruiting class. Brennan has 1,712 career passing yards with 13 touchdowns, six interceptions and 121 completions.
Brennan's name does not yet appear in the NCAA's transfer portal.