Leicester will only consider a record-breaking offer for Wesley Fofana, as Chelsea prepare to make a third bid.
Fofana is a priority target for Chelsea manager Thomas Tuchel, who has seen bids of £50 million and £60m rejected by Leicester already this summer.
Chelsea will have to make the French centre-back the most expensive defender in the world at a fee over £80m to stand any chance of signing him, with Brendan Rodgers revealing his fears over finding a quality replacement.
Though Jamie Vardy is close to signing a new contract to keep him beyond his 37th birthday at the club, Rodgers has admitted the situation with Fofana, 21, remains uncertain.
Leicester have also turned down two offers from Newcastle for England international midfielder James Maddison in the past fortnight.
When asked if there was a cut-off point for Leicester to consider any bids, Rodgers said: "That will be up to the ownership, the end decision will be down to them. Even now, it would be late in terms of looking to get in replacements, but it's certainly something that the later it goes on then the more difficult it becomes.
"At this moment in time we're looking at them being here, working with them, and that's the only focus."
Manchester United made Harry Maguire the costliest defender in August 2019 when they paid Leicester £80m.
Fofana is regarded as a generational talent and is targeting a place at this year’s World Cup with France.
'Vardy still has the appetite and hunger to succeed'
"Another year here for him at least would be really important for his development, but he is quite calm and relaxed in the situation," said Rodgers.
"He is aware of the interest. He understands where we are as a club and where we see him. He’s just getting on with his work and training well, and whenever there is any communication we are able to have a conversation."
Vardy, meanwhile, is set to sign a new two-year deal to extend his glorious Leicester career. The striker’s current contract expires next summer but Leicester have struck a verbal agreement over another extension.
Vardy, 35, has proved a revelation since his £1m move from Fleetwood Town in 2012, winning the Premier League, FA Cup and Golden Boot, while also becoming an England international.
Rodgers said: "He still looks strong, still looks fit and of course we assess that each week as we go along. Jamie is really determined, he has a real appetite and hunger to succeed which is important."
Leicester are close to making their first signing of the summer, with former Cardiff goalkeeper Alex Smithies, 32, in talks over a move on a free transfer.
Boubakary Soumare, the midfielder, is a target for Ligue 1 club Monaco while Jannik Vestergaard has turned down an £11m move to Fulham.