Vinicius, 16, has emerged as one of world football’s hottest prospects.
He starred for Brazil at a South American Under-17 tournament earlier this year.
ESPN Brazil last week claimed that Manchester United and Arsenal were keen to bring the youngster to the Premier League.
But, according to Brazilian outlet Globoesporte , they have been beaten to the punch by Real.
The Spanish giants are said to have agreed a deal in the region of £38m with Flamengo.
They will apparently officially announce the news by tomorrow at the latest.
Vinicius will reportedly head for the Bernabeu next summer when he turns 18.
But Globoesporte say Real could then decide to loan him back to Flamengo for another six months or a year.