Reports in Tuesday's Sydney Daily Telegraph said that the Australian will go under the knife if he does not play in the New Year's Day clash with leaders Chelsea at Anfield.
Liverpool's medical staff are working to get Kewell fit for the match of the day but progress has been slow.
Team-mates say Kewell hasn't trained for a week because of tendinitis in his groin and is unwilling to take painkillers for fear of causing long-term damage.
Surgery would mean Kewell would miss the first leg of the Reds' Champions League last 16 eliminator against Bayer Leverkusen on February 22, but he could be fit for the return in Germany on March 9 and the derby with Everton at Anfield 10 days later.
Kewell would also be cleared to play for Australia at the Confederations Cup in Germany that begins on June 15.
He has already said he is unavailable for the friendlies against South Africa on February 9 and Iraq on March 26.
An operation would provide Kewell with the time he needs to resolve a nagging ankle problem that first flared midway through his debut season for Liverpool, whom he joined from Leeds in August 2003.
Kewell, 26, had Achilles tendon surgery three years ago and David O'Leary, his former manager at Leeds United, says he hasn't been as good a player since.

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