Milan’s first proposal was €15m then they went up to €18m, but neither convinced Saint-Etienne. The Italian club still have an interest in Fofana.
A year ago, Red Bull Salzburg also tried their luck with a €4.5m bid.
ASSE could budge
Saint-Etienne would prefer to keep Fofana for at least one more season before selling him.
However, an offer of €25m from Leicester could tempt the Ligue 1 club, particularly if added bonuses are included.
Saint-Etienne sold William Saliba to Arsenal for €30m last year and would like to bring in more for Fofana.
Alternatively, they could accept a lower fee and include a sell-on clause or accept players in exchange.
Fofana made 24 appearances for ASSE last season, including 14 in the French top flight.