Chelsea, Tottenham Hotspur and Monaco have been linked with the Brazil star, who insists that he will only leave Russia for "a better team".
He told TV Paraiba: "Those approaches [by other clubs] do exist. There are clubs interested in me.
"But if I am to move, it has to be to a better place, with a better team in a better competition. I will be happy too if I stay. Zenit are a great club."
Hulk joined Zenit from Porto last September in a deal worth £52m.