The London side saw a bid in excess of £70million turned down by Leicester last week.
Leicester value the French man at £85million pounds.
Chelsea had thought that their second bid last week would have been enough to acquire the services of the ball-playing center-back.
Chelsea, though, are willing to go as far as £80million with their next bid this week.
This still falls £5million short of Leicester’s valuation.
Leicester’s Head Coach, Brendan Rodgers, has reiterated time and again that Fofana is “not for sale.”
This stance could, however, be put to test when Chelsea’s new bid comes in.
The player in question is reportedly open to a move to Stanford Bridge and frowned at Leicester for knocking back Chelsea’s last bid, which he deems as “enough.”
The questions surrounding this potential sale revolves around whether or not Leicester could reject such a huge amount of cash inflow from Chelsea and how willing they are to keep an unhappy player in the team should Chelsea fail in their transfer drive.