And the Blues are also in talks for RB Leipzig stopper Josko Gvardiol.
Chelsea have had two bids of £60m and £65m rejected for centre-back Fofana. Leicester's original stance was that the 21 year-old was not for sale.
However, the Daily Mail says Leicester will sell for £80m.
The Frenchman has also agreed a contract for around £200,000-a-week with Chelsea.