Liverpool boss Jurgen Klopp has suggested Alisson is closing in on a return from injury after confirming the goalkeeper has started light ball-work in training.
The Brazil international, who was expected to be out for between four and six weeks when he injured his shoulder earlier this month, is doing ball-work outside this week.
Klopp says Naby Keita could play in this week's Champions League clash with Ajax after returning a negative coronavirus test, while Alex Oxlade-Chamberlain is also making good progress from his summer knee injury.
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"Ali looks very good. We have to see; catching balls and stuff like this is all possible, but we cannot rush it and will not rush it," the Liverpool manager said.
"Actually, it's a common thing every day when I see Ali, I say: 'How was it today?' He always, with a big smile, tells me of the slight improvements. Today I didn't see him [yet], so I can't wait to ask for his progress.
"Naby trained yesterday, so that's very positive. We are still learning, we are all learning. about these kind of things when a boy is completely without symptoms, which Naby was.
"He looked very good yesterday in training, to be honest. But I don't know how he looks today, how he reacted - that's much more important then. So, we will see. In the moment, I would probably rather expect him to be involved but I don't know it."
"Oxlade is obviously in a long-term rehab, but looks good and is in a good mood usually."
Liverpool travel to Amsterdam to face Ajax in their first group game on Wednesday, without Virgil van Dijk after it was confirmed he will need surgery to damaged knee ligaments following a clash with Jordan Pickford in the Merseyside derby.
Midfielder Thiago Alcantara also picked up a knock in the draw at Goodison Park but Klopp has not ruled the Spain star out of the Group D opener this week.
"He got a knock, a proper knock," he said. "It's not even close to being as serious [as Van Dijk], but will he be ready for Wednesday? I don't know yet. We will see."
Pitch to Post podcast: Has Van Dijk injury derailed season?
Was Saturday the day Liverpool's title hopes took the cruellest of turns?
Jasper Taylor is joined by Gerard Brand, Ben Ransom and Keith Downie to dissect the weekend's action in the Premier League, leading of course with Van Dijk's ACL injury and what that might mean for the champions.
Sky Sports' Peter Smith:
'The brilliant Dutchman has played in 95 of the 96 Premier League games Liverpool have had since he made his debut in January 2018. He played every minute in the league last season, as they claimed the title for the first time in 30 years.
'So how do they try to cover the absence of a player who has been central to their triumphs domestically and in Europe over the past three years?
'It is a huge task and, with Premier League and Champions League games coming thick and fast, it is a task Jurgen Klopp must get right if Liverpool are to continue to be successful. That is how pivotal Van Dijk has been.'