The Reds will be participating in the FIFA Club World Cup in Qatar during the week when the League Cup last-eight ties are scheduled to take place.
Klopp was asked for an update on the situation on Friday, including the suggestion that two different Liverpool teams could play in the same week.
“I don’t know [when the Villa tie will be held],” replied the manager. “We discussed it already obviously – we have to because there is not too much time to make that decision, but there is no final decision yet.
“If we would play while we are in Qatar that would be two different teams, but we cannot leave any players at home for the Carabao Cup.