Driskel's ankle will be evaluated every day until the game.
Driskel has a sprained ankle and is wearing a walking boot.
"(He's) probably doubtful for this weekend based on the information I have today," (Florida coach Will) Muschamp said. "We'll try to get him on the field Wednesday. If he can't go by then, certainly we'll go with Jacoby (Brissett). We have all the confidence in the world Jacoby will play well."
Driskel injured his ankle in the third quarter of Saturday's 27-20 win over Louisiana-Lafayette.
Muschamp said Driskel's ankle will be evaluated every day.
Before his exit, Driskel completed 13 of 16 passes for 98 yards and a touchdown. Brissett, a sophomore, played well in relief, completing 6 of 8 passes for 64 yards and a score.
Driskel has been solid for the Gators this season. He's completed 64 percent of his passes for 1,324 yards and 10 touchdowns. He's thrown just three interceptions this season.
Driskel is also the team's second-leading rusher. He has 424 yards and four rushing touchdowns on 97 carries.
Florida and Jacksonville State kick off at 1 p.m. ET Saturday. The Gators enter the game at 9-1 and as the No. 6 team in the country. Jacksonville State is 6-4.