The Reds' number one pulled up in the 1-0 win away to Crystal Palace at the start of October, feeling instant discomfort in his hamstring after clearing the ball.
Alisson was forced off and withdrew from the Brazil squad for October's international break which followed shortly after, before also missing the subsequent seven Liverpool matches since.
The 32-year-old was unable to link up with the Brazil side this month either, but that extended period off the pitch has allowed the goalkeeper to step up his recovery from the injury, with a return now in sight.
Liverpool tease potential Alisson return
In a post shared to the club's X (formerly Twitter) account on Tuesday evening, Alisson is seen in full kit following a session at the Liverpool training ground.
That suggests that the Brazilian is inching closer to making a full return following six weeks on the sidelines.
In the seven matches he has been absent, Caoimhin Kelleher has stepped up to deputise and performed well, with Liverpool continuing their fine form despite losing their number one - winning six, drawing away to Arsenal and conceding just six goals.
Manager Arne Slot has confirmed that Alisson will go straight back into the team whenever he is fit though, despite the impressive form shown by Kelleher.
After the recent win over Aston Villa, Slot claimed: "I've always been quite clear and that's always been the position of Alisson that he is, and will be, our first goalkeeper if he is fit.
"But therefore he first needs to be fit, but Caoimhin [Kelleher] has done outstanding last season and this season again as well. But the moment Alisson will be fit he will be our first goalkeeper.
Other injury news concerning Liverpool
Ahead of the trip to St Mary's on Sunday, there are still question marks over a couple of players in the Liverpool squad.
Trent Alexander-Arnold pulled up in the Villa win and was forced off, withdrawing from the England squad shortly after, casting doubt over his fitness ahead of the weekend's fixture.
Mohamed Salah did not join up with Egypt for the recent Africa Cup of Nations qualifiers, but there appears to be no issues with the attacker, as he was also present in training alongside Alisson on Tuesday.
Diogo Jota remains out in attack though, along with Federico Chiesa and Harvey Elliott, who have both missed large chunks of this season so far.