French publication L'Equipe is of the belief that the Blues will pay €40million (£33.2m) for the Marseille striker who will sign a five-year contract with the West Londoners, as reported by Get French Football.
Crystal Palace had lodged a record bid of €38m on Monday, West Ham United had made several new offers on Tuesday, and Tottenham have also been heavily linked but it appears as though the Belgium international is heading for Chelsea.
Additional reports from La Provence suggested that Marseille had agreed a deal with a club, believed to be Tottenham, but have now altered their stance and confirmed that the 22-year-old will be on his way to Stamford Bridge.
RMC indicates that Batshuayi will undergo a medical with the Blues tomorrow, making it quite unanimous where he will end up.
It is believed that Spurs chairman Daniel Levy was 'outfoxed' by Chelsea who agreed a deal with the player in the afternoon, prior to a Tottenham bid in the evening, while West Ham reportedly had a 'total agreement' before Roman Abramovich's right-hand man Marina Granovskaia swooped.
L'Equipe additionally indicated that incoming Blues boss Antonio Conte is a big admirer of Batshuayi and gave his personal go-ahead for the signing.
Furthermore, Canal+ is of the belief that Batshuayi will be joining Chelsea for the aforementioned fee which will surpass Marseille's biggest ever sale of €37.5m when Chelsea signed Didier Drogba back in 2004.
Belgian side Standard Liege will take 35% of the transfer fee for Batshuayi, landing them €14m, while Marseille will take 65% of the Batshuayi fee (€26m).
Batshuayi is currently with the Belgium national team at Euro2016 who are preparing for Friday's quarter-final against Wales in Lille.