Jose Mourinho has reportedly made a £35million move for the Zenit St Petersburg star but the Russian club are said to want closer to the almost £50m they paid Porto in 2012.
Mourinho, who returned as Chelsea manager this week, is also thought to be close to a deal for Bayer Leverkusen forward Andre Schurrle.
However, Hulk could be another man on the Stamford Bridge club's list of targets and the player has always appeared keen on a move to the Premier League.
Hulk is currently getting ready for the Confederations Cup with Brazil but, amid the speculation of Chelsea's bid, he is quoted as saying by Globo Esporte: "If I said there was not anything in it, I would be lying.
"But that is not for now. I am 100 per cent focused on the national team at the moment.
"I came to wear this [Brazil] shirt with pride. My family and my friends are following me. I hope to win the Confederations Cup."
Hulk started Brazil's 2-2 friendly draw against England last Sunday but did not score and was booked before being substituted in the 72nd minute.