The Brazilian, who joined Zenit for a reported 40million euros from Porto in the summer, reacted badly to being substituted towards the end of Wednesday's 1-0 victory over AC Milan in the Champions League.
The result confirmed third place in Group C and Europa League football in the new year, but the 26-year-old admits he may opt to depart the Petrovsky Stadium in the next transfer window.
He told Mediaset Premium Calcio: "I feel good in St Petersburg and my family and son are happy too.
"But if the situation with Luciano Spalletti does not improve, I may have to leave in January. I don't know if my destination will be Italy, anything can happen."
Spalletti gave Hulk's comments short shrift, though, adding: "He can say whatever he wants.
"He may be disappointed, but if I substitute him it is because I am not satisfied with his performance.
"He said that he wants to leave? I don't know what to do about that because I'm staying here."
Portuguese midfielder Danny scored the only goal at the San Siro on Wednesday but Milan head coach Massimiliano Allegri was satisfied with his players' efforts.
He told acmilan.com: "We created a lot of chances and played with good pace but unfortunately we conceded in what was their only chance in the game.
"(Francesco) Acerbi and (Cristian) Zapata played well and conceded very little to Zenit.
"We weren't lacking in commitment, the team played well from a technical point of view even though the motivation can't have been at its highest.
"We didn't deserve to lose though, I'm disappointed for the players but we have to start not conceding goals. Twenty goals in 21 games is too much, we have to do better in certain situations.
"I'm happy with all the individual performances including (Djamel) Mesbah and (Massimo) Ambrosini, who both came back from injuries."