Liverpool boss Jurgen Klopp says his side will not be able to play their Carabao Cup quarter-final if the fixture cannot be rearranged to avoid a clash with the Fifa Club World Cup.
Liverpool beat Arsenal on penalties in the fourth round on Wednesday.
The quarter-finals are due to be played the week commencing 16 December but Liverpool play in the last four of the Club World Cup in Qatar on 18 December.
The EFL say they are in talks with the Reds to identify an alternative date.
Liverpool have been drawn to play Aston Villa away in the last eight.
"If they don't find a place for us, an appropriate place, not 3am on Christmas Day, then we don't play it," said Klopp.
"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 at one point, hopefully it starts now.
"We will not be the victim of this problem. We played [on Wednesday] and we wanted to win. If they don't find a proper date for us then we cannot play the next round and whoever is our opponent will go through - or Arsenal will play it. I cannot change that."
The Club World Cup is held every December and features seven teams from six confederations and Liverpool have qualified courtesy of winning last year's Champions League.
Fifa was "looking forward to welcoming Liverpool in Qatar" for the competition, said a spokesman.
Liverpool are already scheduled to play seven games in December, plus the Carabao Cup quarter-final and either a third-fourth play-off or the final of the Club World Cup on 21 December.
With no midweek slots available in 2019 other than during international breaks, the next feasible opportunity to play midweek - when they will not be competing in the Premier League - will be between fixtures on 11 January and 19 January. But the first legs of the semi-finals are scheduled to be played in the week of 6 January.
Liverpool were due to play West Ham on 20 December in the Premier League and that game is yet to be rearranged.
|Liverpool's fixture pile-up|
|4 December||Everton (h)|
|7 December||Bournemouth (a)|
|10 December||Salzburg (a)||Champions League|
|14 December||Watford (h)|
|16 December||Week of League Cup quarter-finals|
|18 December||TBC (Qatar)||Club World Cup|
|21 December||TBC (Qatar)||Club World Cup|
|26 December||Leicester City (a)|
|29 December||Wolves (h)|
|2 January||Sheffield United (h)|
|6 January||Week of League Cup semi-final first-leg ties|
|11 January||Tottenham (a)|
|19 January||Manchester United (h)|
|* Premier League games unless stated|