The Brazil international hasn’t figured for the Reds since sustaining a calf injury during the Premier League opener with Norwich City on August 9, with Adrian deputising between the posts in his absence.
Alisson has, however, this week began a full training programme alongside his teammates and could come into consideration for the visit of the Foxes.
"With Alisson it's still: maybe, maybe not," Klopp told reporters at Friday’s pre-match press conference.
"Yesterday he trained with the team [for the first time]. But if you know goalie sessions, they are often pretty more intense than the proper football sessions. He looked really good.
"We will see, I have to talk to different people before I make a decision about that.”
He added: "If yesterday would have been the first session for him in training, we would of course not even think about it. And I don't know if we think about it; I have to talk and I didn't [yet]."
Elsewhere, Klopp confirmed Joel Matip remains sidelined with a minor knock, while Xherdan Shaqiri is continuing his recovery from a calf complaint. Both players will, therefore, be unavailable for the clash with Leicester.
Nathaniel Clyne remains a long-term absentee, but the boss reported no other fresh injury concerns following the midweek win over Salzburg in the Champions League.
Third-place Leicester, meanwhile, will have James Maddison available again after he sat out the last two matches with an ankle injury.
Aside from Bartosz Kapustka, who remains sidelined with a long-term knee injury, Brendan Rodgers has a fully-fit squad to chose from.
"James is fine," Rodgers told journalists on Thursday. "He's trained the last couple of days and he's OK. Everyone is fine."
On the meeting with his former club, Rodgers said: "We just want to continue with our performance level. Liverpool are on an incredible run, they are great opponents to test and challenge the quality of our team.
"We're bringing a real positive mindset into our games, no matter who the opponent is."
Last time out
Liverpool 4-3 Salzburg (October 2): Adrian, Alexander-Arnold, Gomez, Van Dijk, Robertson, Fabinho, Wijnaldum, Henderson, Mane, Salah, Firmino.
Leicester City 5-0 Newcastle United (September 29): Schmeichel, Pereira, Evans, Soyuncu, Chilwell, Ndidi, Perez, Tielemans, Praet, Barnes, Vardy.