The deal could break the Asian transfer record of 50 million euros that Jiangsu Suning paid Shakhtar Donetsk for Brazilian midfielder Alex Teixeira in February.
"Zenit have reached a preliminary agreement with Shanghai SIPG concerning the transfer of Hulk, and on Wednesday the player will undergo a medical," Zenit's press officer, Dmitri Zimmerman, told the Russian daily Sport Express.
"Zenit will receive around 56 million euros, while a further 2 million euros could be added to the total price."
Hulk, the 29-year-old who has won 46 caps for Brazil and scored 11 international goals, joined Zenit from Porto in 2012.
He netted 56 goals for Zenit in 97 Russian Premier League matches and was the league's top scorer in the 2014-15 season with 15 goals.
Zenit finished third last season and missed out on qualification for the Champions League. They will play in next season's Europa League.
Shanghai SIPG are coached by the former England manager Sven-Goran Eriksson.
(Editing by Stephen Wood)
