The Merseysiders would be willing to sell the defender, who has played second fiddle to Mamadou Sakho and Martin Skrtel for much of the 2013-14 campaign, for a fee in the region of 14 million euro.
Goal UK reports that Napoli is the front runner to capture the 29-year-old, with boss Rafael Benitez well aware of his talents, having signed him for Liverpool back in 2006 during his time in charge at Anfield.
Agger went as far as saying that he is "no one's third choice" as he continued to be overlooked by manager Brendan Rodgers last season, and he expressed particular annoyance at being left out of key fixtures against the likes of Chelsea and Manchester City.
A lack of playing time has seen Agger's stock plummet considerably, with the former Brondby star having previously been linked with a switch to Barcelona back in August - the Catalans having had a bid rejected by Liverpool, according to Steffensen.
But after making just 16 starts in the league and Rodgers preferring to partner Sakho and Skrtel together at the heart of the defense - with Kolo Toure also selected ahead of the Dane at times - it appears that Agger's time at Anfield is up.
Having signed for Liverpool for a fee in the region of 7m euro back in 2006, the Reds are expecting to make a significant profit on the 29-year-old and have set an asking price of double that, with Napoli the clear favorite to complete a deal.