The former AS Roma shot-stopper suffered a calf injury in the side’s season opener against Norwich City as he was replaced by newly signed Adrian.
With the Reds set to face their domestic rivals Chelsea in the UEFA Super Cup, Alisson will watch the scenario from the sidelines.
Speaking with the club’s official website, German trainer Jurgen Klopp said he is uncertain on the return of his Brazilian goalkeeper, though believes it will not take long for him to be fit for the club.
"[It's] Not too cool. It's a calf injury which takes him obviously out for a while," he told Liverpool's official website.
"I don't want to make now [an] exact prognosis on when he will be back, but it will not be tomorrow for sure, so now then we have to see. It takes a while, it takes a couple [of] weeks for sure, and we have to see.
"I saw already [people saying] six weeks and stuff like this, but Ali was not a lot injured in his career, so I would like to wait a little bit to see how he develops in that process now. But he is not in for the next few weeks."
Since joining Liverpool from AS Roma, Alisson has proven to become one of the best in his position, playing a major part in Liverpool’s run to a Champions League success and also runners-up in the Premier League last season as they were pipped to the title by just a point by Manchester City.
