The central defender could be heading back to his former club after struggling to secure a regular first-team place under Brendan Rodgers last season
Goal understands that Liverpool have been open to selling the 29-year-old since the start of the summer, with Napoli initially interested in a move.
The Denmark international started just 16 games in the Premier League last season and is behind Martin Skrtel, Dejan Lovren and Mamadou Sakho in the pecking order at Anfield.
A statement from Brondby CEO Jesper Jorgensen said: “There have now been speculation in Danish and international media that Brondby is in dialogue with Liverpool FC about a transfer of Daniel Agger .
“Brondby can confirm that there is dialogue with Liverpool FC and Daniel Agger about a move to Brondby. If the club manage to sign Daniel Agger during the next few days, the financial effect of the profit will be limited.
“Brondby IF have no further comments on speculation about Daniel Agger.”