The club have been in talks with the EFL over the possibility of rearranging the match due to its commitments with the FIFA tournament in Qatar.
Liverpool has reached a compromise with organisers that will allow it to select a squad for the Carabao Cup quarter-final that will be entirely different to the group of players who will head to Qatar.
"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," Liverpool said in a statement.
"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."
Although EFL Cup rules state all clubs must play with "full available strength in and during all Cup Competition matches, unless some satisfactory reason is given", the EFL has granted Liverpool leave to name separate squads given the "exceptional circumstances" and the fact that Jurgen Klopp fielded a much-changed line-up in the previous round against Arsenal.
EFL Football Services Director, Dave Cookson, said in a statement: "The EFL is very aware of the challenges clubs face when participating across numerous competitions at home and abroad, and whilst we will always look to work with clubs our overwhelming priority has to be to protect the integrity of the [EFL] Cup and ensure any decisions taken are in the best interests of the competition.
"The EFL has long-acknowledged that this competition provides those clubs with large resources with the opportunity to rotate their squads knowing that teams who wish to be successful have to be prepared to play a large amount of matches over the course of the season.
"Therefore, in these exceptional circumstances, the decision was taken having received clear assurances from the club that there will be a level of consistency in team selection, a feature which is key to ensuring integrity is maintained.
"We recognise the challenges Liverpool face in this matter and appreciate the efforts made to find a practical solution. Finally, I would like to wish the club well in representing the English game at the upcoming FIFA Club World Cup in Qatar."
The Liverpool squad that will stay in England for the clash at Villa Park is expected to be similar to the one used in the thrilling 5-5 draw with Arsenal, a match the Red won on penalties.
James Milner, Joe Gomez, Naby Keita, Adam Lallana, Alex Oxlade-Chamberlain and Divock Origi were the senior players to start that match.
Liverpool is scheduled to play five matches in the space of 11 days from December 10 to December 21: it faces Salzburg in the UEFA Champions League and Watford in the Premier League before the cup meeting with Villa and then two matches at the Club World Cup.
it will then have five days of rest before facing Leicester City away.
The decision keeps Liverpool in both competitions, despite Klopp's warning in the aftermath of the Arsenal game that the club could withdraw if "a proper date" was not found. Rivals Manchester United notably pulled out of the 1999-2000 FA Cup due to their own involvement in the Club World Cup.