Manchester City are planning a £20 million offer for the Dane and are prepared to offer him wages of £100,000-a-week, while Spanish giants Barcelona are also known to hold an interest.
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"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."
Another player being linked with a Liverpool exit is Andy Carroll, with Newcastle and West Ham strongly pursuing his signature.
Rodgers says he has been delighted with the attitude shown by the England striker and understands his desire to get regular first-team football.
"Between now and the end of the window there are going to be players feeling a little bit unsure and insecure,” added Rodgers.
"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."