The 18-year-old is regarded as one of Brazil’s top young prospects having made his first-team breakthrough at Vasco earlier this year.
Santos has attracted widespread interest from clubs across Europe including Paris Saint-Germain, Barcelona, Newcastle United and Manchester City.
But according to Globo, Chelsea have now agreed to pay Vasco a €20 million (£17.5m) fee to sign Santos.
The report claims that the midfielder is now due to travel to London to undergo a medical and sign a contract.
Santos had signed a contract extension with Vasco in September which keeps him tied to the club until 2027 and includes a €50m (£43.8m) release clause.
Santos has represented Brazil’s national side at under-16 and under-20 level.
According to reports in France last month, PSG had been pushing hard to sign Santos but the midfielder was convinced about making the move to Chelsea.
Graham Potter’s side could be in the market for new midfielders next summer as both Jorginho and N’Golo Kante see their contracts expire at the end of the season.
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