Tottenham, Chelsea, Manchester City and Burton will not learn the dates of their Carabao Cup semi-final second legs until after the FA Cup fourth-round draw on 7 January.
The EFL says it is being held up by a "complicated and congested fixture schedule" with Premier League and FA Cup ties to also consider.
The organisations are working closely to reach an "acceptable solution".
The second-leg ties will be played during the week beginning 21 January.
Tottenham play Chelsea in the first leg on 8 January (20:00 GMT) and City take on Burton on 9 January. (19:45).
What is the current situation?
Tottenham and City have league games scheduled for 20 January and would prefer to avoid playing their EFL Cup second-leg tie on 22 January.
However, if either club were asked to play on 24 January, their potential involvement in the FA Cup fourth round on 26 or 27 January would have to be considered.
On 29 January, Newcastle play City in a televised league game which cannot be rescheduled.