There is hope that Alisson will return for the game against Manchester United on 17 December, but there is a chance that such a timeframe is slightly optimistic.
As a result, Kelleher, who has been Liverpool's first-choice goalkeeper in the cup competitions this season, will come into the side, playing his first Premier League minutes of the season against Fulham this Sunday.
Speaking in his press conference before the match with the Cottagers, Klopp was quick to reaffirm the faith he has in 25-year-old Kelleher, someone he describes as an "exceptional, exceptional talent".
Talking about whether Kelleher was up to the challenge of being a regular starter, Klopp said: "Yeah, no doubt. No doubt. We see him every day in training. He is an exceptional, exceptional talent.
"Maybe we don’t mention his name often enough, but it is a John Achterberg [Liverpool's goalkeeper coach] thing. From day one when I am in, he told me this will be our homegrown boy who will make it.
"Since then, we see every step. He was a boy and now he’s a man. And yeah, top goalie, no doubt."
Klopp added: "He is in general a focused person. You will not see him in a bar celebrating the clean sheet [against LASK]! That is not a problem. Caoimhin is prepared for that, he wants that now.
"We had discussions in the summer about it, obviously, but as long as we don’t have a solution we cannot loan players. He is homegrown and all these kind of things, so we have to make sure first and foremost, the first responsibility is we do the best for Liverpool and then we have to see how we can sort it.
"Now, obviously, for him it is the situation he didn’t want to have [Alisson being injured] but obviously somehow, yes, because he wants opportunities, he wants to play and now he will get a few games, definitely. And I trust him."
Kelleher was impressive for Liverpool during their 4-0 win over LASK on Thursday and will need to channel his inner Alisson in the next few Premier League matches, starting with Fulham on Sunday.