Centre-back Agger left Brondby to join Liverpool in January 2006 and has made over 200 appearances for the English giants.
Liverpool's close-season signing of Dejan Lovren has seen vice-captain Agger fall further down the Anfield pecking order, though, with Martin Skrtel and Mamadou Sakho often preferred to the Denmark skipper.
At just 29, a return to Brondby would be surprising, but club chairman Jan Bech Andersen claimed they would do "everything in our power" to sign Agger earlier this month.
And their bid to re-sign Agger has gathered momentum, with the Superliga club announcing on Saturday that they were in talks with Liverpool.
"Brondby IF can confirm that there is dialogue with Liverpool FC and Daniel Agger about a move to Brondby IF," a club statement read.
Brondby finished fourth in Superliga last term but have bolstered their squad with the acquisition of Johan Elmander in June.
