"We have to see -- not day by day, he will not play tomorrow [Thursday], not on Sunday, probably not the week after. Then it should be kind of OK," Klopp said.
That timeline would likely see Liverpool's No.1 miss Premier League games against Fulham, Sheffield United and Crystal Palace. Klopp will hope Alisson will be fit in time for their game against Manchester United at Anfield on Dec. 17.
Liverpool also expect to be without forward Diogo Jota, who has picked up a muscle injury, for several weeks.
"Diogo will take a little bit longer, we don't know exactly how long, but it's a bit more severe. We have to see," Klopp said.
A win or a draw in Thursday's Europa League game against LASK at Anfield would confirm Liverpool's place in the knockout stage of the competition.