The Reds were beaten 3-2 by the Premier League champions in the fourth round of the Carabao Cup in a memorable game at the Etihad.
It was a strong Liverpool team Klopp fielded, with the likes of Mo Salah, Darwin Nunez, Thiago Alcantara and Andy Robertson in the starting XI.
However, Alexander-Arnold and Van Dijk were not involved, despite not having known injuries, but Klopp explained why they were absent afterwards.
‘Trent was ill, like Ox [Alex Oxlade-Chamberlain] was until yesterday. Virgil trained today. All the others should be available apart from the long-term injuries.
‘The only one who is not here is Ibou [Ibrahima Konate] who will come next week.’
The long-term injuries Klopp refers to are Luis Diaz, Diogo Jota, Roberto Firmino and Arthur Melo, while Curtis Jones is close to a return.
However, there was another injury worry for Klopp which emerged on Thursday, with James Milner going off with a hamstring problem in the first half, replaced by Nat Philipps.
Klopp said: ‘Milly felt something in the hamstring. We hope it’s not an injury but he felt something. He doesn’t think it’s a lot but we will see.’
Liverpool are back in action on Boxing Day when they travel to take on Aston Villa in the Premier League as part of a very busy schedule after the World Cup break.
Klopp’s side host Leicester City on 30 December before going to Brentford on 2 January.
For more stories like this, check our sport page.