The clubs have been in protracted negotiations for the centre-half, who has been a long-term target of the Blues.
It is understood there has finally been a breakthrough in those talks six days before the transfer window closes.
Fofana has been made to train with Leicester's Under-21s after Foxes boss Brendan Rodgers revealed he was not in the right frame of mind to feature against Southampton last weekend.
The 21-year-old Frenchman has made 52 appearances for Leicester since joining from St Etienne in October 2020.
Out of those games, Fofana has played 37 times in the Premier League.
The player also helped the Foxes to FA Cup glory in 2021 - his only piece of silverware with the club.
Chelsea are also understood to be continuing their pursuits of Everton winger Anthony Gordon and former Arsenal skipper Pierre-Emerick Aubameyang.