The 29-year-old centre-back has made over 200 appearances for the club since arriving from Brondby in 2006, but the signings of Mamadou Sakho and Dejan Lovern over the past two seasons have seen him fall out of contention for a regular starting place.
Said to be desperate to leave Anfield, the Denmark international was linked to Barcelona earlier this summer, prior to the Catalan giants signing Thomas Vermaelen, as well as with a £12 million move to Atletico Madrid, but a reunion with his former manager could now be on the cards.
However, negotiations have not been without their problems, with the Serie A side preferring a loan deal, having struggled to match both Agger’s wages and the £10 million asking price.
With Liverpool, on the other hand, determined to sell, the potential move could therefore hinge on whether Napoli can manage to offload fellow centre-back Miguel Britos in order to raise funds.
There reportedly remains the faint option of a return to Brondby, but Benitez, who first brought Agger to Merseyside and managed him until his departure in 2010, is said to be determined to bring his former defensive stalwart to Italy.