Portugal international Jota, who has scored nine goals in 17 appearances since his £41million move from Wolves in September, injured his knee in the 1-1 Champions League draw at Midtjylland on Wednesday.
"Yeah, it's worse than we first thought and better than we then thought," manager Jurgen Klopp told Sky Sports ahead of Liverpool's visit to Fulham.
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"All the potential surgeons had a look on it, no surgery needed. But he will be out for a while. We don't know exactly but one and a half, two months. We don't know exactly.
"It's pretty similar with (full-back) Kostas Tsimikas, by the way. Unbelievable.
"It was first after the game. We saw the situation when he got it; him himself, nobody would have thought something happened there.
"We got him off the pitch and he said 'I feel a little bit' and next day, scans and then a surgeon has to look at it.
"That's how we do it, different information. In the end, it's strange but we were happy that we heard the final diagnosis."
Klopp has had to manage an injury crisis during the club's Premier League title defence.
Defenders Joe Gomez and Virgil van Dijk have suffered long-term injuries and Alex Oxlade-Chamberlain sustained a knee injury during the pre-season training camp in Austria.
Goalkeeper Alisson Becker, skipper Jordan Henderson, Thiago Alcantara and Trent Alexander-Arnold have also been sidelined for parts of the campaign.
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