Bagent played four snaps and completed his lone pass attempt for a six-yard gain in Sunday's 38-13 loss to the 49ers.
Bagent is slated to start Thursday's Hall of Fame Game against the Texans, Courtney Cronin of ESPN.com reports.
Following the selection of No. 1 overall pick Caleb Williams, Bagent is viewed as the favorite to open the season as the Bears' QB2, USA Today's Vincent Parise reports.
Bagent didn't see the field in the Bears' 17-9 loss to the Packers on Sunday.
Bagent (illness) has no injury designation ahead of Sunday's game against the Packers.
Bagent (illness) did not participate at practice Wednesday.
Bagent is expected to start Thursday's game against Carolina after the Bears listed Justin Fields (thumb) as doubtful on their final injury report, Mike Garafolo of NFL Network reports.
Bagent completed 18 of 30 passes for 220 yards with two touchdowns and three interceptions in the Bears' 24-17 loss to the Saints on Sunday. He also rushed eight times for 70 yards and lost a fumble while recovering another.
Coach Matt Eberflus said Monday that Bagent will start Sunday's game at New Orleans, Brad Biggs of the Chicago Tribune reports.
Bears head coach Matt Eberflus said Monday that Bagent will remain the team's starting quarterback for next Sunday's game against the Chargers, Brad Biggs of the Chicago Tribune reports.