The Reds beat Arsenal in a thrilling clash on Wednesday and are now set to face Aston Villa in the last eight.
However Jurgen Klopp’s side are due to be in Asia for the Club World Cup when the quarter-finals are due to be played.
Klopp alluded to Liverpool potentially pulling out of the Carabao Cup if a suitable date could not be found.
Liverpool’s clash with Arsenal ended 5-5 before the Reds won on penalties.
And following the match, Klopp said: “It shows the problem we have in the Premier League that no one cares about things like this, so that’s how it is.
“The competition is there, we play the game, if we have no time for the next round we cannot change it.
“FIFA tells us we have to go to the Club World Cup, the Premier League tell us we have to play in the Carabao Cup so we try to play it, but if we don’t find time it will not happen in our winter break or whatever they give us, because we need that.
“So, I don’t care to be honest. It just shows what the problem is. Everybody wants us to play constantly, we’ve just thought about tonight – we’re not thinking about the next round.
“If they don’t find a place for us, an appropriate place, not 3pm on Christmas Day or something, then we don’t play. They have to make it.
“You have to think about these things – if you have a fixture list, where one team cannot be part of all the games, then you have to think about it.
“Hopefully it starts now. I think it’s fair that this problem is obvious now. We will not be the victim of this problem.
“We played tonight, we want to win it, if they don’t find a proper date for us, we cannot play the next round and whoever our opponent is will go through, or Arsenal.”
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