Liverpool have not decided whether they will sign a centre-back in January.
The Reds have won their last two games without star defender Virgil van Dijk, who will likely miss the rest of this season with an ACL injury.
They have been linked with Schalke's Ozan Kabak and Dayot Upamecano of RB Leipzig.
With the impressive performances of Fabinho at centre-back, Klopp might take his time in finding a long-term solution at the position.
Talk of Kabak joining the Reds has been rubbished by Anfield sources, who believe the news is being pushed by an "exuberant agent".
Brighton defender Ben White was scouted last season, but the Seagulls asking price has deterred Liverpool from pursuing a move.