ESPN understands that Liverpool will only consider an offer of £25 million for Denmark international Daniel Agger, who has been targeted by Premier League champions Manchester City.
Liverpool sources have confirmed that City have made approaches over Agger, 27, but that the two sides are some way apart in their valuation of the player, who has two years left on his contract.
Anfield manager Brendan Rodgers said: "Daniel's a top player, and any manager will tell you that they don't want to lose their best players. But I suppose we've seen it at every club - every player has a price.
"For me, Daniel is a top-class professional. I've really enjoyed working with him and speaking with him over the last few weeks.
"You're going to have your top players linked with other clubs, but I'm not forced to sell anyone and Daniel is a very important player. But you can never say never, and I'm a realist as well. We'll see what happens between now and the end of the month."
With talks over a new deal for Agger having stalled, City have made their interest known and indicated that they would be willing to go as high as £18 million for the centre-back - but that falls well short of Liverpool's valuation.
It is thought, though, that the Merseysiders would find it difficult to resist a bid of £22 million - the same fee Manchester City paid Everton for Joleon Lescott in 2009.
With the two sides still to find a compromise, England winger Adam Johnson could be used as a makeweight to smooth out a deal.
Agger was omitted from Liverpool's squad for last week's Europa League qualifier with Gomel in Belarus, which many saw as an indication of an impending departure.
Although the club and Rodgers insisted that it was purely down to concerns over fitness, Agger's agent, Per Steffensen, said his client was "not injured in any way".
Meanwhile, Liverpool are hopeful of securing a £15 million deal for Swansea midfielder Joe Allen in the days to come, despite Swans manager Michael Laudrup insisting that he is worth £20 million.