The French youngster is regarded as a strong possibility to bolster Madrid's defence if the club manage to part company with their out-of-favour players
The France Under-20 international has been strongly linked with a new challenge after establishing himself as a key member of Le Havre, who finished Ligue 2 in ninth place last season.
Lille and Paris Saint-Germain are both understood to be keen to take Fofana to the top tier of French football, while Premier League duo Aston Villa and Newcastle have also been suggested as possible destinations.
However, Real Madrid's interest could prove to be crucial to decide the future of the player, who will captain his country's Under-20 squad at the upcoming World Cup, in Colombia.
It is reported Real Madrid are lining up a bid for Fofana if they manage to cash in on Lassana Diarra and Fernando Gago, who have both been linked with the exit door.
The Copa del Rey holders have already dipped into the French market this summer, having signed Raphael Varane from Lens.