Dossena has played in just one Premier League match this season, taking the field for a whole minute against Bolton back in August, and is now third choice behind Emiliano Insua and Fabio Aurelio.
Related ArticlesBenitez to 'walk through storm'Rafa Benítez lacks striking optionsFive seasons on the brinkLyon facing problems ahead of Liverpool gameLiverpool 'should have signed Nicolas Anelka'Sport on televisionAccording to the Sun, Napoli coach Walter Mazzari is keen to sign Dossena on loan in January until the end of the season, with a view to signing the player permanently.
However, the major stumbling block to any permanent move will be the full-back's £40,000-a-week salary.
Meanwhile, Steven Gerrard has said he was "devastated" when Xabi Alonso left Liverpool and admits the club have missed the Spaniard.
Liverpool captain Gerrard forged a good understanding with Alonso in midfield.
Alonso moved on to Real Madrid in the summer, since when Liverpool have struggled for form in the Premier League and Champions League.
It was a move which hit Gerrard hard. "Devastated, yeah. Devastated. But there was nothing I could do about it," he told FourFourTwo magazine.
"Xabi said a long time ago that he wanted another chapter in his career and finally he got it and his team-mates and the coaches couldn't stand in his way. We just have to say thanks and move forward without him."