The reigning Premier League champions City have been linked with Agger, with Roberto Mancini, the manager, aiming to strengthen his squad before the transfer window closes.
City rate the 27-year-old central defender at £18 million (Dh103.5m).
That sum may not be enough to persuade Liverpool to sell, but Rodgers said Agger could go if City come back with a higher offer.
"Every player has a price and top centre-halves are at a premium," said Rodgers.
"Thiago Silva has left AC Milan for PSG [Paris St Germain] for £40m. He [Agger] is one of the leading players in European football, so it is going to be a big valuation. 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."
Rodgers also confirmed Craig Bellamy, the Welsh forward, has asked to leave Liverpool to join the Championship side Cardiff City.
"We've been in talks with him and with Cardiff, in terms of a possibility of him going back there," Rodgers said. "It's not him crying wanting to leave Liverpool, it's more compassionate reasons, really."
Rodgers said Bellamy, who represented Britain, at the London Olympics, wanted to be with his family who still live in Cardiff.
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