The offer is worth around £28.25m at 9am on Friday morning but that is set to change as the exchange rate fluctuates following the Brexit vote.
Batshuayi scored 24 goals for Marseille in Ligue 1 last season and is attracted by a move to the Premier League, but he said last month that he would not change clubs until after Euro 2016.
He has been an unused substitute for their three Group E games at Euro 2016.
WATCH: West Ham bid £28m for Marseille striker Michy Batshuayi.
Transfer Centre: https://t.co/Mp3BfYOvkI https://t.co/Uo3IIwkbLH
— Sky Sports News HQ (@SkySportsNewsHQ) June 24, 2016