Both players missed Thursday’s Carabao Cup defeat by Manchester City, Van Dijk following his World Cup exertions and Alexander-Arnold due to illness.
But Jürgen Klopp expects the former to be available and hopes the latter will be too for Monday’s Premier League game at Villa Park.
Roberto Firmino and James Milner will be absent from the Reds’ matchday squad, however.
Firmino picked up an injury in training earlier in the week, while Milner sustained a hamstring issue at Etihad Stadium. Alex Oxlade-Chamberlain is available, though.
Klopp said on Friday: “Millie didn’t get better since then – he will be out for a couple of games. Same for Bobby.
“Bobby, it’s like this, he is already on the better side of it, even when it is only a few days ago, but it’s not a major thing, so we will look day by day with him.
“Ox is fine, Ox was ill, like Trent, some of the staff as well. That’s why we have to be careful in the moment, absolutely, like everybody, I think it’s going around.
“That makes planning really difficult for the next game because we were 100 per cent clear what we want to do against City and then you have to change in the last second pretty much, that’s not cool but it’s the situation and that might happen against Aston Villa as well so we need to be flexible, stay flexible.
“Apart from that, Virg trained now obviously completely normal so will be there. Trent hopefully will be better; he was not part of the full session but of parts, let’s see how that develops until tomorrow. That’s it.”
Ibrahima Konate, meanwhile, will return to training with the Reds after the trip to Villa, having helped France reach the World Cup final.
Villa will be without World Cup-winning goalkeeper Emiliano Martinez following his success with Argentina, with Robin Olsen set to deputise.
“I want him [Martinez] to rest now because after the big emotion, after the hard work he did, he has to have some days off to rest,” head coach Unai Emery told the media.
“Next week he is coming back to start with us.
“The idea is to start with Olsen, he is here to replace Emiliano or to compete with him.
“He has a small problem, but I think he is going to train tomorrow [Saturday] as normal and if nothing changes, he is going to be ready on Monday.”
Midfielder Jacob Ramsey (hamstring) is also sidelined for Villa, with defender Diego Carlos a long-term absentee.
Former Red Philippe Coutinho missed their last three fixtures before the World Cup due to injury but has now returned to training.
Last competitive match
Brighton & Hove Albion 1-2 Aston Villa (November 13): Martinez, Cash, Konsa, Mings, Digne, Kamara, Luiz, McGinn, Ramsey, Buendia, Ings.
Manchester City 3-2 Liverpool (December 22): Kelleher, Milner, Gomez, Matip, Robertson, Bajcetic, Thiago, Elliott, Carvalho, Salah, Nunez.