"We expect him to return to practice by midweek this week," Saban said, per ESPN's Alex Scarborough. "I don't know what he'll be able to do or how much. But that's sort of the prognosis for where we are right now."
Tagovailoa suffered a high-ankle sprain during a 35-13 victory over Tennessee on Oct. 19. He did not play in Saturday's 48-7 victory over Arkansas.
It should not come as a major surprise that Tagovailoa is nearing a return to the field, given a previous update provided by Saban.
"He's absolutely doing even better than expected," Saban said during an SEC Nation interview (h/t AL.com's Matt Zenitz). "Didn't have a lot of swelling this time around, so that sort of accentuates the ability to rehab. He's doing well."
Prior to the injury, Tagovailoa had put himself right in the thick of the Heisman Trophy race. He had completed 74.7 percent of his passes for 2,166 yards and 27 touchdowns while throwing only two interceptions in seven games.
Alabama was able to handle business without its star quarterback on Saturday. Making his first career start, sophomore Mac Jones completed 18 of 22 passes for 235 yards and three touchdowns. Taulia Tagovailoa, Tua's younger brother, also saw some action, completing six of eight passes for 45 yards.
Saturday's victory came against an Arkansas (2-6) team that is in last place in the SEC West, having yet to win a conference game in five tries.
The Crimson Tide's next opponent? No. 2 LSU (8-0) on Nov. 9.
Led by Heisman Trophy front-runner Joe Burrow, the Tigers have already defeated three teams that were ranked in the Top 10 at the time of the meeting (No. 9 Texas, No. 7 Florida and No. 9 Auburn). LSU is averaging 46.8 points per games through eight games, so having Tua Tagovailoa ready for that showdown figures to be top priority in Tuscaloosa.
Alabama now has a bye week, giving Tagovailoa two weeks to try to get his ankle healthy enough to play.