Virgil van Dijk suffered damage to his anterior cruciate ligament in the Merseyside derby and will undergo surgery.
The Dutch defender was hurt by a rash challenge from Everton goalkeeper Jordan Pickford - but was not awarded the penalty the Reds thought was deserved due to the officials adjudging him offside.
Liverpool manager Jurgen Klopp had already admitted the prognosis for the 29-year-old was "not good".
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And the club confirmed that an operation will be required.
"No specific timescale is being placed upon his return to action at this stage," they said in a statement. "Following surgery, Van Dijk will begin a rehabilitation programme with the club’s medical team to enable him to reach full fitness as soon as possible."
Van Dijk took to social media later on Sunday to share his own message, thanking fans for their concern and support, and adding: "I'm now fully focused on my recovery and will do everything I can to be back as quickly as possible."
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