According to L’Equipe, Leicester offered €32m and a 10% sell-on clause for 19-year-old Fofana on Monday night.
Once again though, it was turned down by Saint-Etienne, who value their young centre-back highly.
Earlier this month, after an earlier approach was knocked back, the Foxes offered €25m for Fofana.
ASSE boss Claude Puel wants Fofana to stay and develop, but the youngster has expressed interest in a move to England.
Fofana has again been showing his quality in the early days of the new Ligue 1 season.
In his three appearances, Saint-Etienne kept clean sheets and won 2-0, including a win over Marseille.
However, he was mysteriously absent from their fourth match of the season against Nantes on Sunday.
Leicester eye Tah
With a deal for Fofana proving difficult, Leicester are considering Jonathan Tah as an alternative.
Tah has lost his starting place at Bayer in the past year and Leicester could ask for him on loan with an option to buy.
With Euro 2021 coming up, Tah wants to make sure he is playing regular football this season.
24-year-old Tah has made 10 appearances for Germany, most recently featuring against Switzerland this month.