The 28-year-old joined Zenit from Porto in 2012 and has scored 44 goals in 92 appearances for the three-time Russian champions.
With his previous contract due to expire in 2017, the club have moved to agree an extension with the Brazil international.
Since moving from Porto, where Hulk won four Primeira Liga titles, three Taca de Portugal ties and the UEFA Europa League, the 28-year-old has yet to win silverware in Russia.
However, with Zenit leading the top flight by seven points and still in contention for the Europa League - he could end that drought this season.
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