Jurgen Klopp has reportedly grown increasingly frustrated with Liverpool's transfer policy despite the current owners believing that they have done the best they could considering the current financial climate.
The German was desperate to bring in defensive reinforcements before the February 1 deadline and the Reds managed to sign centre-backs Ben Davies and Ozan Kabak from Preston North End and Schalke 04 respectively.
Koulibaly, 29, has been linked with a move away from Italy over the last few seasons and is valued at around £100m by club owner Aurelio De Laurentiis - a fee the Reds would be unwilling to pay.
Instead, Liverpool opted to recruit cheaper alternatives with Davies arriving for a fee believed to be around £2m, while Kabak joined on loan for the remainder of the season with an option to make the deal permanent in the summer.
Koulibaly, who has been at Napoli since 2014, has made over 270 appearances for the club, including 25 in all competitions this campaign.