West Ham had submitted a bid of €35 million for the Marseille striker, but the rapidly falling value of the pound means the deal now has some question marks over it.
The pound has plunged to a low which has not been seen since 1985 after the United Kingdom voted to leave the EU.
West Ham had made Batshuayi one of their top targets this summer, but there are now apparently serious concerns over the deal.
The Hammers are known to be on the hunt for new additions this summer, with Slaven Bilic aiming to sign a new front man.
Batshuayi scored 21 goals for Marseille last season after playing 45 times in all competitions.
West Ham have already completed two signings this summer, following the additions of Sofiane Feghouli and Havard Nordtveit, but Bilic is expected to continue to invest over the coming months.