The Daily Mirror is reporting that the Reds are likely to be able to secure the signing of the 26-year-old Italy international from the Serie A side as Emre Can heads for the exit at Anfield.
The same report says that both Manchester United and Arsenal are also interested in the midfielder but it is Liverpool FC who are leading the chase for his signature ahead of the summer.
The story also claims that Napoli currently value Jorginho at around £50m as the summer transfer window draws ever nearer.
He has been in good form for the Serie A side this season, scoring two goals and making four assists in 26 league games for Napoli.
The Brazil-born midfielder holds both an Italian and Brazilian passport, and the same article says that he would be keen on a move to Anfield because of the success of the likes of Philippe Coutinho and Roberto Firmino at the club in recent seasons.
Liverpool FC are bound to be linked with a host of players in the coming weeks and months as the summer transfer window gives Jurgen Klopp the chance to significantly add to his squad.
The Reds will return to Premier League action after the international break with a trip to Crystal Palace on 31 March.
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