The clause will be inserted to fend of interest from mega-rich clubs, with the likes of Paris Saint-Germain linked with luring the star away.
Vinicius, 21, enjoyed a stellar campaign at the Santiago Bernabeu, finishing the season with 22 goals and 20 assists in 52 games across all competitions.
The Brazilian played a key role in helping the Spanish champions regain the LaLiga title with several matches to spare.
He also scored the all-important goal as Los Blancos defeated Liverpool 1-0 in the Champions League final in Paris last month, as Madrid secured their 14th triumph.
According to Marca, he is now set to sign a new long-term deal to remain in the Spanish capital following his impressive performances under Carlo Ancelotti.
An agreement between all parties is understood to be close, with an official announcement expected in July.
The deal will see Vinicius become one of the club's best paid players, doubling his wages from £2.77m per year to £8.67m.
A four-year deal is the pipeline, but it is the remarkable release clause which is the most eye-catching part of the new deal.
The player already has a clause of £300m, but this will increase to a staggering £870m.
This is expected to stop Europe's riches, who are funded by the nations of Qatar and Saudi Arabia, respectively, from trying to secure Real's star man.
Vinicius made the move to Los Blancos from Brazilian side Flamengo in 2018 for £38m.
During his four years at the club, he has netted 36 goals and contributed to 43 assists in 170 appearances to date.