Naby Keita is close to returning for Liverpool but Jurgen Klopp is unsure when Alisson will be ready to replace Adrian in goal.
Alisson has been out of action since he suffered a calf injury in the Reds' opening 4-1 Premier League win over Norwich City in August.
Klopp initially indicated the European champions are expected to be without the Brazil international for the "next few weeks".
Speaking ahead of Saturday's home Premier League game against Newcastle United, Klopp issued an update on Alisson and midfielder Keita.
"Funnily enough, we had lunch again so he looked good," Klopp told reporters of Alisson's progress.
"He's improving but as normal we cannot put any pressure on it. It was a really serious injury in the calf and it is now much better of course.
"That's good for us, good for him, but we don't know exactly. The target was always after the next international break he could be ready, but we don't know.
"That's no pressure on it. Hopefully everything will be fine for the rest of the season, that's the plan.
"Naby is close, much closer than Ali. I think he could be in training when we come back from Napoli next week [in the Champions League].
"Clyney [Nathaniel Clyne] and [teenage striker] Paul Glatzel are obviously far away still but doing big steps. It looks quite okay at the moment."
Liverpool are top of the Premier League table having taken maximum points from their first four games of the season before the international break, a run that saw Klopp claim the August manager of the month award.
Mohamed Salah and Sadio Mane were among the Reds stars given a break from international duty, which was welcomed by Klopp.
"It was perfect for the boys who didn't have to go," Klopp added. "There's always that challenge.
"I'm really happy boys being named for their national team, it's really nice, a big honour and all that stuff but I've said it 500 times - if you see the players who didn't have to go this time, for different reasons, everything is different.
"It's in a very intense period to have five or six days off. They train, they always train, but they don't have to be here and we do proper football sessions because usually we only have three players here and it makes no sense, this time we could have had five.
"Could have trained but it still makes no sense - then Sadio and Mo would not have had the time off they needed. It's really tough always to have two games when we speak about the international break, then they have another week with two games which is not easy.
"But we can't change that so we don't think too much about it. They are refreshed, that's how it is, hopefully we can use that."