According to reports, the Blues submitted an offer on Friday, with journalist Fabrizio Romano saying it's worth 'in excess of £70m', however, he notes Leicester insist the 21-year-old is not for sale.
Chelsea are keen to add strength to their back line, having signed Marc Cucurella from Brighton for £60m and this latest rumour saw '£70m for Fofana trending', while Gary Neville tweeted his surprise at the reported fee.
The young Frenchman has been at Chelsea since 2020 when he moved from Saint-Etienne.
His manager, Brendan Rodgers has talked him up, saying he could be one of the best in the world.
"When he said that it obviously adds extra pressure but it has to be the aim for any player," he told The Telegraph. "I want to not only win trophies but try to be the best defender in my position in the world."
And despite the initial proposal being rejected, The Guardian claim Chelsea believe £85m will be enough to land Fofana.
This would take the spending of Thomas Tuchel's side to more than £200m, having also signed Gabriel Slonina, Raheem Sterling, Kalidou Koulibaly and Carney Chukwuemeka.
Pierre-Emerick Aubameyang has also been linked with a move to Stamford Bridge as has his Barcelona teammate Frenkie de Jong.
The club have not made much on exits, with Romelu Lukaku going to Inter on loan, though he brought in a fee of around £7m. Antonio Rudiger and Andreas Christensen left in free transfers and Levi Colwill has moved to Brighton on loan, though Armando Broja has been linked with a £30m move to West Ham.