The Danish defender has been a key player for the Reds in recent campaigns, yet his first-team importance was diluted somewhat last term.
The form of Martin Skrtel and the presence of 2013 signing Mamadou Sakho saw Agger benched for much of the campaign, and Rodgers opted against recalling him to his starting XI on many occasions despite multiple wobbly displays from the Merseysiders.
Italian giants Napoli – managed by former Anfield chief Rafa Benitez – are thought to be frontrunners for his signature after being linked with a move during January.
The current Naples side’s boss brought Agger to Liverpool in 2006, and is known to be a huge admirer of his abilities.
The player himself has also hinted that he may be forced to move on after revealing that he perceives Rodgers to not see him as “good enough” to start.
A lack of playing time may limit the Scandinavian’s list of suitors, with the likes of Barcelona thought to have cooled their interest in recent times.