MatchLiverpool v Arsenal: Carabao Cup team news
The goalkeeper was forced to miss the Reds' last two fixtures after testing positive for COVID-19, with Caoimhin Kelleher deputising between the sticks.
But Jürgen Klopp reported on Wednesday that Alisson and Trent Alexander-Arnold (COVID-19) had resumed full training ahead of the Anfield tie.
Thiago Alcantara and Divock Origi will remain sidelined for the 7.45pm GMT kick-off due to injury, however.
"Caoimh is the goalkeeper for this competition but there is a chance Ali will play tomorrow just because of the situation we were in," the boss explained.
"I think he needs the game now. We will see how we decide it finally but there is a good chance that Ali will play tomorrow just because of the situation with COVID and everything, when he was out.
"We all need to make sure the boys have as much rhythm as they can get. So there's a good chance Ali will start tomorrow."
Klopp added: "Robbo got a little knock in the Shrewsbury game but is fine. I'm not sure if I forgot anybody but the rest are available."
Liverpool will be unable to call upon Mohamed Salah, Sadio Mane and Naby Keita, who are competing at the Africa Cup of Nations in Cameroon.
Arsenal are also represented in the tournament by Pierre-Emerick Aubameyang, Thomas Partey, Mohamed Elneny and Nicolas Pepe.
Emile Smith Rowe and Takehiro Tomiyasu both sat out the Gunners' defeat by Nottingham Forest in the FA Cup last weekend due to minor muscle issues.
Folarin Balogun and Granit Xhaka were forced to miss that clash after testing positive for COVID-19. The former has since moved to Middlesbrough on loan, while the latter will be assessed ahead of the trip to Merseyside.
"It is extremely volatile and uncertain," boss Mikel Arteta told reporters. "I don't know what the situation is that we will have today or if it is different to yesterday. Obviously I cannot get into any detail with that.
"But it is what it is. In the last week or so we lost so many players for many different reasons and we are trying to adapt to that. I will use the players that we have and make the most out of it.
"Obviously after having COVID they are going through that illness in a different way. Some of them are having symptoms, some are being affected, some are struggling in their first few training sessions and some of them are completely fine.
"So as soon as we have the option to train Granit fully with the team, we will see where he is at. I don't know where he will be physically."
Last match
Liverpool 4-1 Shrewsbury Town (January 9): Kelleher, Bradley, Konate, Van Dijk, Robertson, Fabinho, Morton, Dixon-Bonner, Gordon, Jones, Woltman.
Nottingham Forest 1-0 Arsenal (January 9): Leno, Cedric, White, Holding, Tavares, Lokonga, Patino, Saka, Odegaard, Martinelli, Nketiah.
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