The 18-year-old is in no rush to leave Ligue 1, despite reported interest from Russia and the Premier League
The 18-year-old is believed to have caught the eye of the big-spending Russian club, while Premier League sides Chelsea and Arsenal have also been credited with an interest in his services.
But the France youth international, who is currently competing in the Under-20 World Cup, is happy to remain in Ligue 1 and continue to his footballing education.
"If Kurt stays with Saint-Etienne next season then he will continue to grow. He does not have a fierce desire to leave," his agent told le10sport.com.
The centre-back, who has a contract with les Verts until June 2017, echoed the sentiments of his representative when quizzed by L'Equipe over his future.
He said: "Anzhi?" I have heard some rumours but I know nothing else. I do not want to talk about my future. For now I will play in the World Cup and focus on the game against Turkey and then after we will see what happens."
Zouma helped Saint-Etienne to a fifth-place finish in Ligue 1 last season.