Reds boss Jurgen Klopp is rumoured to have already held personal talks with the Senegal international over a summer switch.
Koulibaly has been linked to numerous clubs during his six years at Napoli, but the Serie A outfit's asking price of near €100m has often put off other teams.
However, Emanuele Cammaroto of Napoli Magazine has claimed that Liverpool have found a way around that issue by proposing a player-plus-cash offer.
Divock Origi is thought to be the player Klopp is prepared to part company with in order to soften a deal for Koulibaly, meaning that the Reds value him at just under £40m.
Liverpool's domestic rivals Manchester City and Manchester United have also been tipped to move for Koulibaly.