The Reds defender has only made one substitute appearance in the Premier League so far this season and is finding it difficult to prove his worth to manager Rafa Benitez.
With Napoli looking to bolster their defence during the January transfer window, Dossena's agent Roberto La Florio thinks the left-back may want to move to ensure a place in the Italy squad for next year's World Cup.
"It is clear that in January Napoli will sign new players, especially in the role of Dossena," said La Florio.
"We'll see in January if there are opportunities to return to Italy and play - we are interested because Dossena wants to go to the World Cup.
"Napoli is the Italian team that has pushed most for Dossena and according to me it would be the perfect solution for him."
The 28-year-old became the first Italian player to play for Liverpool when he signed at Anfield for £7million in July last year.
Dossena is currently recovering from a muscle injury but may make the bench for the Reds' UEFA Champions League trip to Lyon on Wednesday.