As Champions League winners, Liverpool will be playing in the last four of the Club World Cup in Qatar on 18 December, with the Carabao Cup quarter-finals scheduled for the same week.
The EFL released a statement in reply to the Liverpool manager's comments, saying: "The EFL is in discussions with Liverpool to identify an alternative date given the club's participation in the FIFA Club World Cup competition."
Colchester have secured a lucrative trip to Manchester United, and the League Two club will be looking to cause further upset, having already knocked out top-division sides Tottenham and Crystal Palace in the competition's earlier rounds.
Manchester City, in search of their third successive league cup trophy, will travel to Oxford, after easing past Southampton on Tuesday in the fourth round.
Leicester will travel to Everton, who have never won the competition, after a 3-1 win at Burton on Tuesday.
The quarter-finals, aside from the Liverpool fixture, are set to take place the week starting December 16.
Full List:

Liverpool Vs Aston Villa
Manchester United Vs Colchester
Manchester City Vs Oxford
Leicester Vs Everton
