Klopp has been dealt a defensive crisis on Merseyside this season, potentially losing first-choice centre-back pairing Virgil van Dijk and Joe Gomez for the rest of the season.
Van Dijk damaged his ACL in the Reds’ 2-2 draw away at Everton last month, shipping a heavy challenge from Toffees goalkeeper Jordan Pickford which left him needing surgery.
And to add to Klopp’s woes, Gomez sustained a knee injury of his own this week on international duty with England and is expected to miss a “significant part” of their remaining fixtures this term.
While the 23-year-old is said to have undergone successful surgery, the usual rehabilitation period for his ruptured patellar tendon is around six months.
Joel Matip is now the only senior centre-back available for Klopp, meaning he could be forced to deploy youngsters Nat Phillips and Rhys Williams until the January transfer window opens.
Fabinho was also used as a makeshift central defender before sustaining a hamstring injury in last month’s Champions League win over FC Midtjylland.
According to The Mirror, Klopp was already planning to dip into the January transfer market for a new centre-back before his latest blow in the shape of Gomez.
Schalke ace Ozan Kabak was reportedly on his radar, yet the Turkey international is only 20 years old and considered more of a prospect for the medium term.
With Van Dijk and Gomez sidelined, the Premier League champions need a ready-made, experienced man to come in at the turn of the year - and Koulibaly is also believed to be of interest to Klopp.
The Napoli star, who is widely regarded as one of the most talented defenders in European football, enjoys a close relationship with Senegal team-mate Mane and could therefore be tempted to join him at Anfield.
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The pair also spent a season together with French outfit Metz before leaving to join Genk and Red Bull Salzburg respectively in the summer of 2012.
Koulibaly has made 249 appearances in his time at Napoli, scoring 10 goals and winning the 2019/20 Coppa Italia.