Napoli signed the veteran striker on a free transfer last summer but has not played a league game for the Serie A giants since January.
The San Paolo-outfit are prepared to sell him in the ongoing transfer window and Llorente has been listening to offers from several clubs.
Genoa, Benevento and Parma are interested in signing him in the ongoing window, but for the moment none of those offers interest Llorente.
According to Italian broadcaster Sportitalia, the 35-year-old striker has rejected all the approaches from clubs in Italy and he wants to leave Serie A.
Llorente wants to move away from Italy and has offers on his table from clubs in England, Germany and Spain.
West Ham have been linked with an interest in the striker and David Moyes is keen to add more experience to his squad.
It remains to be seen whether the Hammers make a firm offer to land Llorente, especially with him willing to leave Italy.
The Spaniard had a spell in England with Tottenham Hotspur before he left the club last summer.