The former Schalke man picked up a "little problem" as Liverpool fell to a fifth straight Anfield defeat when they hosted Chelsea on Thursday.
Kabak now joins the likes of Virgil van Dijk, Jordan Henderson and Joe Gomez on Liverpool’s lengthy injury list and is now a doubt for Sunday's clash.
Speaking after the game, Klopp said: "We had the problem that Nat Phillips would play with Ozan [Kabak] but couldn't play," per Daily Mail.
"So now do we take an unexperienced pairing on the pitch or do we take Fabinho? We decided for Fabinho."
"Now Ozan yesterday, after the game, had a little problem after playing a lot of games and we will see if he's ready for Fulham – it doesn't look like it at the moment."
Ozan Kabak gradually growing into the Liverpool squad
After suffering injuries to several key defensive players, Liverpool completed a deadline-day move for Schalke’s central defender Ozan Kabak, alongside Ben Davies from Preston North End.
The 20-year-old has had a shaky start to life at Liverpool, making his debut in the 3-1 defeat to Leicester City.
He followed it with more assured performances against Leipzig and Sheffield United, when he was paired with both Jordan Henderson and Nathan Phillips at the heart of the defense.
On Saturday, he was the more solid of Liverpool’s central defensive pair, as Fabinho struggled with the pace of Chelsea’s attack.
Liverpool have now added another name to their growing list of defensive absentees, with club captain Jordan Henderson set to miss six weeks of action, while Van Dijk and Joe Gomez are ruled out for the rest of the season.
Liverpool will be aiming to end their dire home run when they take on Fulham at Anfield on Sunday. They will follow it up with a clash with RB Leipzig three days later in the second leg of their Champions League last-16 tie, after grabbing a 2-0 win in the reverse leg.