The Reds head to the King Power for a lunchtime kickoff this weekend, on the back of a miserable 4-1 loss to Man City last time out.
Fabinho had missed three games prior to that clash, but returned to play the full 90 minutes at Anfield, though the Brazilian was clearly short of sharpness as Liverpool struggled.
Now, he will be absent for at least another game, with Klopp revealing that he “will not be available” to take on Brendan Rodgers’ side.
“He suffered again a little muscle issue, so will be out for this game,” the manager told reporters on Friday.
“We have to find a solution. All of them had the chance this week to show who’s ready, so I have to make a decision tomorrow.”
That decision could include one or both of Kabak and Davies – deadline-day signings who are yet to play a minute of football so far – with the Schalke loanee the more likely to start.
It could serve as preparation for the trip to Budapest to play RB Leipzig on Tuesday night, as Klopp added: “I don’t know [when Fabinho will back] in the moment, I really don’t know.”
If either are called upon, it will be a “proper challenge” against Jamie Vardy, but Klopp believes a week on the training pitch at Kirkby has steeled his new centre-backs for action.
“Jamie’s obviously a proper challenge in this league. The way he plays, the way he gets set up by his mates. That’s a proper job to do,” he continued.
“But we can only do it, always, with the whole team. That’s how we always tried to do it. We have to avoid the passes to him.
“Jamie is a world-class player for sure in this specific area of the pitch, with his speed, that’s really tricky.
“With [Kabak and Davies], obviously we now had some sessions together where we could really work on this defensive setup, and that’s very, very important.