The 34-year-old is out of contract after leaving Flamengo, and could be set to join the Tigers on a free transfer.
His agent Jonathan Hassall said: "Juninho is not in the country at the moment but he will hold talks with Hull, maybe tomorrow.
"He has offers from Italy and Brazil as well as Qatar and Kuwait.
"England is where his heart is but we will need to wait and see how things go when we meet with Hull."
Juninho won the 2002 World Cup with Brazil, had two spells with Boro and one with Celtic, as well as playing in Spain and hsi home country during an illustrious career.
Hull City have called a press conference for 11am tomorrow morning, which may be used to announce a new signing.