Vinicius was approached by Saudi Public Investment Fund (PIF) officials to inquire about his interest in moving to the Saudi Pro League (SPL) on a five-year contract worth around 200 million euros (£171.2m) per season fixed, plus bonuses.
The package would also include a separate 10-year contract to become an ambassador for the 2034 World Cup, which is set to be held in the country, but those terms and financial numbers are yet to be discussed.
Although an official, formal offer has yet to be presented, Vinicius has not dismissed the move and gave permission to PIF to approach Real Madrid.
Despite being "happy and motivated" in the Spanish capital, Vinicius and his representatives believe that a lucrative offer like this needs to be studied carefully.
Another source close to the player said that Real have shown no interest in negotiating a transfer, highlighting the player's one billion euro (£860m) buy-out clause.
Real Madrid and PIF did not respond to requests for comment.
Obsessed to be taken seriously as a football force, the Kingdom of Saudi Arabia announced a Sports Clubs Investment and Privatisation Project, with PIF taking ownership of 75% of the capital of the country's four main clubs: Al-Ahli, Al-Ittihad, Al-Hilal and Al-Nassr.
The biggest Saudi transfer came from the country's most successful club, Al-Hilal, who spent 90 million euros (£77m) to buy Neymar from Paris Saint-Germain.
With Karim Benzema at Al-Ittihad and Cristiano Ronaldo at Al-Nassr, PIF tried to persuade France captain Kylian Mbappe to be the big name Al-Ahli was still missing last year.
The forward, however, turned down Saudi Arabia's lucrative offer and joined Real Madrid in June.
The proposal for Vinicius is understood to be similar to the Mbappe offer. The Brazilian would join Al-Ahli, linking up with former Premier League stars Riyad Mahrez and Roberto Firmino.
Vinicius, who is under contract until 2027 after signing an extension in 2022, is a contender to win the Ballon d'Or after helping Real to a Champions League and La Liga double last season.
