The Reds' no.1 goalkeeper appeared to have a problem with his hamstring late on in their 1-1 draw at Manchester City.
Alisson was able to complete the rest of the match but now looks set for a period on the sidelines as he recovers.
Diogo Jota also picked up an injury away at City and was substituted as a result, with Klopp providing updates on their current statuses.
Speaking ahead of their Europa League clash at home to LASK, he said: "Both are out.
"With Ali it's a bit lesser so we have to see. Not day by day, he cannot play tomorrow, not on Sunday [against Fulham]. Probably not the week after, then it should be kind of okay.
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"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."
Alisson is therefore set to miss Premier League clashes against Fulham, Sheffield United and Crystal Palace as a result of his injury.
He will also be absent for the visit of LASK on Thursday and potentially their final Europa League Group E match against Union Saint-Gilloise.
Caoimhin Kelleher is normally named in goal for Liverpool's European matches and was linked with a move away in the summer.
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However, he has remained at Anfield and Klopp hinted that situations such as this with Alisson is a contributing factor as to why.
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"Yes, that's pretty much exactly it. That's why we knew we wanted to have Caoimhin here for these moments.
"Nobody, Caoimhin as well, wanted Ali to get injured, but if these things happen then you need the strongest possible option and that's Caoimhin for us.
"That's the only positive about that, to be honest, that we can put in Caoimhin. That's fine.
"Now he gets an opportunity that he deserves, he would have played tomorrow night anyway, that's clear, but now he will have a few more games and hopefully he can show his full potential."