The Reds have already turned down a £15m offer from Barcelona last week.
With Manchester City having a £20m bid for Real Madrid's Pepe rejected, it is looking likely that a similar offer for Agger will be forthcoming.
It is almost exactly a year ago when City last attempted to lure the Danish defender to the Ethihad. Rodgers stood firm then, saying: "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."
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