The powerful attacker is considering his options after several clubs showed their interest in luring him away from his current club.
The 26-year-old joined Zenit from Porto in the summer of 2012, but has endured a mixed time in Russia, with early reports of dressing room unrest as a result of his large salary and an unsavory racism storm involving the club's supporters.
As a result, he could be on the move again ahead of the 2013-14 campaign, with Monaco and Chelsea closely monitoring his situation.
"I have received some offers. A number of clubs are interested in me. But if I do leave, it has to be a step up to a better club and a better league," the attacker told TV Paraiba. "I am happy to stay here, though, if a transfer does not materialize. Zenit are a great club and I am happy here."
Hulk's contract with Zenit runs until June 2017.