A verbal agreement has been reached between the two parties.
Sky Sports News has been told that the fee is for £70m plus add-ons, but the details of the structure of payments and exact terms of add-ons are still to be determined.
The fee is not likely to go over £75m. The personal terms between Fofana and Chelsea will not cause any problems.
Possible replacements are being looked at byLeicester.
Brendan Rodgers confirmed on Thursday that Fofana, who missed last weekend's defeat to Saints amid the speculation over his future, would not be available for Saturday's game.
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The player was training with the club's U23s after failing to show up for a training session last week.
Rodgers said that he wouldn't be available for the weekend and had trained with the U23 squad.
The players and the team are my focus. I have enough energy to keep going. It will be done with the clubs. We have to work with what we have
Between now and the end of the window, hopefully there will be some transfer business done. It would be great for the team to be able to improve their squad. We will continue to work with what we have.
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The third bid for Fofana was immediately rejected.
Sky Sports News described the additional payments as "ambitious", even though the offer was thought to be £60m.
Two previous bids in excess of $60m were rejected.
The transfer window will close at 11pm on September 1st.
Sky Sports has a dedicated Transfer Centre website where you can keep up-to-date with all the latest news. Sky Sports News gives you the ins, outs and analysis of sports.