The pair both picked up knocks in the 1-1 draw away at Premier League champions Manchester City in Saturday's early kick-off.
Brazilian goalkeeper Alisson suffered a suspected hamstring injury in the closing stages as he hit the deck holding his leg following a goal kick, though he did manage to continue until the end.
Portuguese forward Jota had to come off in the second half, though, with what appeared to be a muscular problem.
And speaking to talkSPORT after the full-time whistle, Klopp has hinted they could be without the pair for quite some time.
He said of the pair: "It looks like we've lost Ali with a muscle problem and Diogo Jota.
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"And that is massive. I don't know how many games coming up now [until Boxing Day], maybe 15 [ten].
"We have to get through this, we have to improve, we need to get more stable and in games like this, we should be more compact."
Liverpool travel to Austria next week to take on LASK in the Europa League, before Premier League clashes against Fulham, Sheffield United and Crystal Palace.
They then face Union Saint-Gilloise in Belgium in Europe's second-tier competition, where they then host rivals Manchester United at Anfield on December 17.
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To complete their festive fixtures, they then welcome West Ham in the Carabao Cup, before entertaining Arsenal two days before Christmas.
In his post-match press conference, Klopp declared that Alisson and Jota will now undergo scans to determine how long they will be out for.
He stated: "The shadow on this game is obviously that Ali felt something and Diogo felt something - something we have to assess and then we will see."
On Alisson, he added: "I hope it's not that serious, but I don't have the answer - no clue in the moment what it is.
"I spoke to him and he said he only felt [it] a little bit, but we have to wait for the scan."