The Reds created a fixture issue when they beat Arsenal on penalties to reach the quarter-finals of the Carabao Cup, in which they are due to take on Aston Villa at Villa Park.
That game is scheduled for Tuesday December 17 with a 7.45pm kick-off.
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Less than 24 hours later, the Reds are due to play the semi-finals of the Club World Cup, a competition they qualified for by winning last year's Champions League.
The club had hoped that English football authorities might be able to give them some leeway on when to schedule their domestic fixture, but Liverpool confirmed today that no compromise had been reached.
"We will be utilising two playing squads simultaneously, with one squad participating in the FIFA Club World Cup in Qatar and another in the Carabao Cup," the statement said.
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"The club would like to take this opportunity to underline that while this is not an ideal scenario, it is an outcome which was arrived at with the best interests of the competition, our fellow clubs and ourselves as the sole motivating factor.
"We would like to thank the EFL for their efforts to accommodate us and we can confirm alternative dates were discussed, but ultimately none were considered suitable without compromising the scheduling of the competition itself or placing an undue strain on our playing staff."
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An EFL statement on the matter meanwhile said: "The EFL has been engaged in discussions with Liverpool for a number of months regarding the possibility of needing to find a suitable date for the club to meet its commitments to the Carabao Cup, as well as the FIFA Club World Cup.
"Having considered all possible scenarios, the EFL has now accepted a request from the club to play the fixture on the scheduled date, during the designated week for the quarter-finals in the domestic fixture calendar, with Liverpool committing to fielding a team that is largely consistent with those that have participated in earlier rounds of this season’s competition."