Vinicius, 16, made his professional debut for the Brazilian giants on Sunday (AEST), coming on against Atletico Mineiro.
The forward is tipped to join Madrid, with reports in Spain suggesting a deal is done for the teenager to make a €45 million ($66.7 million) move in June 2018.
Flamengo announced a new deal for Vinicius on Tuesday (AEST), with a salary readjustment and increase in his release clause from €30 million ($44.5 million) to €45 million ($66.7 million).
Vinicius has starred at youth level for Flamengo and for Brazil's Under-17s.
He scored seven goals for his victorious Brazil side in the South American Under-17 championships earlier this year.