The 27-year-old only moved to Anfield from Udinese last summer but failed to impress in the Premier League, starting only 19 matches in all competitions for Rafa Benitez's side.
Napoli are leading the chase to sign Dossena, whose agent, Federico Pastorello, told TuttoNapoli.net: "Their offer is of five million Euros plus bonuses - the clubs are in negotiations and we are awaiting news.
"The player is currently in Singapore with Liverpool and he is also awaiting news.
"Although he loves being at a great club like Liverpool, he would welcome the opportunity to join Napoli.
"We are very keen to find an agreement. Napoli know how much he earns, but first the two clubs have to strike a deal."
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