The Reds continue to spend as much time fending off rumours regarding reported outgoings as they do possible incomings.
Agger is among those being heavily linked with a summer exit from Anfield, with the Denmark international said to be attracting interest from Barcelona.
Liverpool, however, have no plans to offload a man widely regarded as one of the finest centre-halves in world football.
Taking that into account, Rodgers has made it clear to any potential suitors that it would take big money to lure Agger away from Merseyside.
“Daniel is a top player and you do not want to lose your best players,” he said.
“He has been here seven years. He loves the club and its supporters.
“But every player has his price and we will see where it goes.”
Speculation also suggests that Carroll could soon be on the move, with West Ham believed to be leading the chase for his signature.
Rodgers continues to offer vague responses to questions about the England international, with the Reds boss refusing to rule Carroll in or out of his plans for the forthcoming campaign.
“Between now and the end of the window there are going to be players feeling a little bit unsure and insecure,” he said.
“There is a new manager and more players to come in.
“But Andy has been terrific. He knows exactly where he stands. He is like everyone else. He has to fight for their position. There are not many clubs you could go to and be a guaranteed starter.
“I understand Andy wants to play games. But he really enjoys it here.
“I have had a number of conversations with him and we will see how that develops.”