The Brazilian has been in impressive form for Carlo Ancelotti's side during the 2021-22 campaign, scoring nine times and contributing seven assists in 16 appearances in all competitions.
Vinicius still has four years left to run on his contract, but he is believed to be one of the lowest earners at the Bernabeu, and Los Blancos are allegedly keen to hold talks over a fresh deal.
According to ABC, Real Madrid want to raise the attacker's release clause to €1bn (£860m) and are prepared to hand him a six-year contract with a rise in salary.
Vinicius recently revealed that he is determined to sign a new deal with Los Blancos, who could allow Isco, Gareth Bale and Marcelo to leave the club on free transfers next summer.
The South American has now scored 23 goals and registered 30 assists in 134 appearances for Real Madrid since making the move from Flamengo in July 2018.