The Anfield boss revealed the Premier League champions' interest but insists he is unwilling to part with the Dane on the cheap after Thiago Silva's recent eye-catching transfer
Goal.com exclusively revealed that if Rodgers does lose Agger, he will line up a move for Atletico Madrid centre-back Diego Godin.
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"Daniel is one of the leading centre-halves in Europe," Rodgers told reporters.
"There's been contact from City but it's nowhere near his value. You can only consider something like that if it is going to benefit you.
"Of course, you might lose a top player but if it benefits you going forward — and you can make two or three steps forward because of it — you may have to consider it.
"But we don't want to sell him so unless someone comes in with a ridiculous offer, there's no way I want to lose one of my best players."
The Northern Irishman went on to reveal that he would use Thiago Silva's recent £40m move from AC Milan to PSG as a guide when pricing up he Dane.
"Thiago Silva has left AC Milan for PSG for £40million. He [Agger] is one of the leading players in European football, so it is going to be a big valuation," he continued.
"Is he a player I want to lose? No. He understands how I want to work and can play a real pivotal part in how I want to play.
"But I am a realist. If someone comes in with a massive bid and it is in the best interests of the club, whether it is Daniel or any other player, you have to look at it."
The 39-year-old also reassured fans from Merseyside that Agger does not want to leave after speaking to him when he took over the helm at Anfield.
He added: "There's always rumour, particularly in this period. It's just a shame the window does not shut as the season starts.
"But Daniel and I have had a number of conversations so he knows where I am at, he knows where the club are at and he doesn't want to leave, which is great. In my first conversation with him at the Euros he made that quite clear.
"He loves the club, loves the fans, so that was music to my ears — but we'll see."