Chamberlain limped off with an ankle injury 15 minutes from time in last Sunday’s FIFA Club World Cup final against Flamengo.
Liverpool edged the Brazilians 1-0 after extra-time but the victory came at a cost with Chamberlain’s latest injury.
Liverpool are away at second-placed Leicester City on Boxing day before hosting Wolverhampton Wanderers on Sunday, but Chamberlain will play no part in those games.
"With Oxlade-Chamberlain - the ankle is what we expected," Klopp said.
"You have three ligaments on the outside the ankle and one of them is damaged. We have to see how quickly we can fix that.
"I don't know [how long that will take] exactly, I had the injury myself, but that was years ago.
"It can take a while or it can be quicker we have to see but no chance for Thursday, and this year Oxlade-Chamberlain will not play anymore that is clear. We have to see how quick it can settle. That's it."
Klopp however provided better news for Liverpool fans regarding injuries to Fabinho, Dejan Lovren and Joel Matip.
Klopp added: "Matip, Lovren and Fabinho are in a really good way but are not ready for these games."
Liverpool are 10 points clear of Leicester City, and victory on Thursday over Brendan Rodgers’ men will extend their lead to 13 points with a game in hand.
