The 29-year-old sustained the damage in a challenge with Son Heung-min in the 3-1 victory over Tottenham last Thursday.
The severity of Matip’s injury, plus long-term injuries to Virgil Van Dijk and Joe Gomez, has meant Klopp’s side have moved late in the January transfer window to sign Davies permanently and Kabak on loan.
“Unfortunately, we found out now after everybody looked at it that Joel will be out for the rest of the season," Klopp told Liverpool’s official website.
“But he will be ready for the start of the next pre-season and finally everything will be sorted.”
Davies, meanwhile is delighted with his “surprise” move to Anfield.
“I’m obviously delighted to be here," Davies said. “It’s a huge opportunity.
"Obviously it came as a bit of a surprise when it first came but once you start to get your head around it, the opportunity that is in front of me is incredible. I’d be silly to not make the most of it and learn off the players [at the club].
“I’ve never actually been to Anfield and I haven’t had a look around yet. I had a quick look out and had a look at the pitch and it looks like carpet, which obviously you’d expect.
“I haven’t actually walked out of the tunnel yet, so I’m looking forward to that. Just to be in this kind of atmosphere is brilliant.”
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