The Danish centre-back has been a key member of the Reds’ first-team since signing for the club in 2006 under Rafael Benitez and was made vice-captain when Jamie Carragher retired last year.
But the 29-year-old was far from ever-present in Brendan Rodgers’ XI during 2013/14 , with the Northern Irishman often opting to use Martin Skrtel and Mamadou Sakho during the season’s climax.
Now it is understood that the Merseysiders are attempting to find a new club for the classy defender, and have offered him to a host of top European sides.
One outfit to have been presented with the opportunity is Barcelona, who have chased the Scandinavian in the past.
Napoli are also being mooted as an option given that Benitez is in charge of the Italians, while Manchester City have been linked with Agger in recent years.
Liverpool appear to be closing in on a deal for unsettled Southampton centre-back Dejan Lovren after tabling a £20m offer.