"It's still day-to-day, and you don't know what's going to happen tomorrow or the next day, but he's moving around well and throwing the ball with confidence," Saban told ESPN's Chris Low. "His mobility will be the big question, but every day that's improved dramatically."
Tagovailoa is recovering from a right ankle injury that knocked him out of an Oct. 19 win over Tennessee and kept him on the shelf against Arkansas the next week. He dealt with a similar injury to his left ankle last year but hasn't experienced as much swelling this time.
"If you watched (Tuesday's) practice film, you would have a hard time even recognizing that the guy is hurt," Saban said. "But we're not asking him to do everything he would in a game. He's not scrambling for a first down. He's not getting chased by a defensive end or any of that stuff, so it's a little bit controlled. We'll continue to monitor him and see how he progresses, but we're pleased with where he is."
The Crimson Tide are gearing up to face LSU in a matchup that will pit the top two teams in the AP Poll against each other. Alabama is third in the College Football Playoff rankings, while the Tigers are second.
Saban cautioned that the Tide won't take any risks with their Heisman Trophy hopeful, who's expected to jump to the NFL at the end of the year.
"We've been focused on making sure we get both guys (Mac Jones and Tagovailoa) ready to play as best we can," Saban said. "I'm not going to put Tua in a situation that could be detrimental to him or his future."
Tagovailoa has thrown 27 touchdowns against two interceptions over seven appearances this season. He led Alabama to a win over LSU last season, throwing for 295 yards with a pair of touchdowns and one interception. He also rushed for a touchdown in that game.