Real Madrid are understood to have improved their offer to the Brazil star during meetings at the club's training ground.
Arsenal are interested in the forward, who has entered the final year of his deal, and are watching the outcome of his contract talks closely.
Sky Sports News has been told there is already a great relationship between Vinicius and his new head coach Jose Mourinho.
This has played a big role in the positive direction of the talks over his future this summer.
Mourinho is adamant he wants Vincius to be one of the protagonists in his Real Madrid team.
Arsenal agree £75m fee for Guimaraes
Arsenal have agreed a £75m fee with Newcastle for their captain Bruno Guimaraes.
He has been given permission to travel for a medical.
Guimaraes told Newcastle bosses earlier this summer that he wanted to join Arsenal if a suitable offer arrived.
Arsenal's opening bid was rejected but the 28-year-old now looks set to join the Premier League champions.
Guimaraes, who joined Newcastle in 2022 from Lyon for £40m, has made 195 appearances for Newcastle, scoring 31 goals.
Newcastle had been keen to ensure Guimaraes, who has two years left on his contract plus a club-held option for a third, remained at the club but if this deal goes through as expected, they will have made more than £240m from player sales this summer.
Anthony Gordon joined Barcelona in a £69.3m deal and Spurs signed Sandro Tonali for £100m, while manager Eddie Howe also departed in what has been a turbulent summer at St James' Park.
