The bid in the region of £70million was turned down on Tuesday evening.
Leicester remain adamant that their valuation of the defender, in excess of £80million, must be met for the transfer to be completed.
Chelsea remain optimistic, though, that a deal can still be struck and sources say that another bid will be prepared by the London club soon again.
The French defender is thought to be enthusiastic about moving to Stamford Bridge and reasons that the valuation placed on him is “too high.”
Personal terms between Fofana and Chelsea has already been agreed for weeks now.
Chelsea look light at the moment in defence after seeing Rudiger and Christensen leave this transfer window.
The purchase of Fofana is, therefore, viewed as a high priority for Chelsea as they seek reinforcements.