Tagovailoa returned from a high-ankle sprain to play in last week's loss to LSU, but Saban told reporters there's lingering pain that could prevent him from facing the Bulldogs.
"He's got soreness in his ankle from playing in the game (against LSU)," he said. "Just like a lot of players this time of year, you've got to manage the practice. You've got to manage the reps. Just like last week, it'll probably be a game-time decision as to whether he can or can't play. ... It's just kind of day-to-day."
Saban explained the Heisman Trophy contender didn't suffer a setback and isn't dealing with a new injury, but the team will wait to see how his ankle responds by Saturday.
"We did all the medical research that you could do on him to find out if he did any damage or hurt himself (against LSU) in any way shape or form, and he did not," he said. "So we'll manage the soreness. ... We'll just have to manage it day to day, and he should respond each and every week. The situation that he's in is very much expected, and he doesn't have any further issues."
Tagovailoa missed a blowout victory over Arkansas after getting injured Oct. 18 against Tennessee. Alabama had a bye week before facing LSU.
The 21-year-old Hawaii native put together a strong performance against the Tigers. He completed 21 of his 40 throws for 418 yards with four touchdowns and one interception, but it wasn't quite enough, as fellow Heisman hopeful Joe Burrow led the Tigers to a 46-41 win.
Mac Jones would draw his second start of the campaign if Tagovailoa is ruled out. He connected on 18 of his 22 attempts for 235 yards with three scores and no picks in the win over the Razorbacks.
"I felt really prepared, and we were prepared," Jones told reporters after that game. "It's football, and I've been playing since I was five. Everybody around me has been playing since they were five, so no big deal."
Alabama faces Western Carolina, an FCS opponent, next week, so if Tagovailoa sits this week, he'll likely be sidelined again for that contest to get him as close to full strength as possible for the regular-season finale against Auburn on Nov. 30.
That said, the Tide have no margin for error in their quest to earn a College Football Playoff berth, which makes Tagovailoa's availability for the Mississippi State clash more vital.