The Daily Star says the recruitment of a new striker is a priority for the north London side, as they only have Jermain Defoe on their books at present.
Villas-Boas knows Hulk well, having managed him during his time at Porto.
The Portuguese coach was also rumoured to be keen on bringing the 25-year-old with him to Stamford Bridge last summer, after he was appointed Chelsea boss.
The Blues are reported to still retain an interest in £35m-rated hit-man, as they look for a replacement to Didier Drogba up-front.
But they will fear that Villas-Boas's relationship with the player could see them fall behind in the pecking order for the powerful forward.