Liverpool's preparations for Saturday's Premier League meeting with Sheffield United received a boost, with Alisson in contention for a return.
The Brazilian goalkeeper hasn't played since the champions' 3-1 win over Arsenal at the end of September.
It had been feared that Alisson could be out for as long as eight-weeks, but manager Jurgen Klopp says the 28-year old is among a clutch of players to be assessed ahead of the Blades' visit to Anfield.
"So, let me say it like this with the others, apart from Ox and Virg, obviously, and maybe Kostas, who gets closer and closer but is not at all in contention for this game or the next one," Klopp told his pre-match press conference.
“All the others, we have to see day by day pretty much. It’s a lot of conversations with the medical department – for who it makes sense, for who it is too early and all these kinds of things.
“That’s the time we are in with the games we have; if somebody is injured for two weeks that could mean five games and it is still not a serious injury.
“So, I don’t know in this moment who will be available. My last information was that the boys who played the other night, they are all fine.
“They are OK and the rest, we will see.”
Thiago Alcantara and Joel Matip, who both picked up knocks in the drawn Merseyside derby, are the others who could feature having missed the trip to Ajax.
Klopp wasn't giving a timescale on Virgil van Dijk's recovery from an ACL injury.
"Virgil was here, he’s OK. But about when the surgery will happen and stuff like this, I don’t think it makes sense that we give pretty much a time schedule every day," the manager said.
“But it will be fine and will happen in an appropriate time. So, that’s it pretty much – he is as good as possible