The German outfit's general manager Klaus Allofs confirmed the club's interest in the French youngster, but admitted that his price tag could prove an obstacle.
"Kurt Zouma is a player who, of course, we are somewhat interested in," he told Braunschweiger Zeitung.
"He has great skill for the future. We have enquired if there is a chance to sign him.
"Given the proposed transfer fee, we would have to find out if there is a realistic chance for him to play first-team football at our club."
Zouma is under contract with Saint-Etienne until 2017, but has attracted interest from across Europe.