As revealed by skysports.com last week, City have seen two bids rebuffed by Liverpool for Denmark international Agger.
City are expected to come back with a third bid with Roberto Mancini keen to bring the central defender to the Etihad Stadium.
Barcelona are also thought to be watching Agger’s situation at Anfield with talks over of a new deal at Liverpool seemingly coming to nothing.
Agger’s future has been the subject of speculation for some time and rumours intensified after he was left out of the squad for last week’s Europa League victory over FC Gomel.
Liverpool were hoping to keep hold of Agger, but it seems they could cash in on him if City up their bid to £20million, freeing up funds for Brendan Rodgers to strengthen the squad elsewhere.
Rodgers is already thought to be drawing up a list of defensive replacements for Agger should City meet their valuation for the 27-year-old.