The 16-year-old is one of Brazilian football’s hottest prospects, having represented his country at U17 level.
Both Real Madrid and Barcelona are also said to be interested in the playmaker.
But Italian newspaper Gazzetta dello Sport claim Flamengo have already tied Vinicius down to a contract with a huge release clause.
According to the report, he is being compared to Neymar in Brazil and Flamengo are determined to keep him for the time being.
So keen are they to do so that they will not negotiate with other teams unless a fee is paid up front.
Former Flamengo president Kleber Leite last month revealed that Unite officials had spoken to the Brazilian side’s general director Fred Luz about a deal for Vinicius.
“[Luz] told me that he was contacted a while ago by a representative of Manchester United, who wanted to discuss the possibility of them having priority for a transfer,” Leite said.
“The talks didn’t get far, because Fred Luz told them plainly that future discussions would depend on the immediate payment of a sum that would give them priority among offers of equal value.
“At that point, the Englishman, who thought it was going to be a piece of cake, left and didn’t return.”
Scouts from Real Madrid and Barcelona were both reportedly spotted at the South American Under-17 championship.
Brazil won the tournament with the help of Vinicius, who finished as top scorer with seven goals.