The centre-forward, who is not wanted at the Stamford Bridge club, could link up with ex-Chelsea manager Frank Lampard at Goodison Park.
According to talkSPORT, Batshuayi is a key target for Everton as they seek to add competition for Dominic Calvert-Lewin.
The Belgian international will serve as a replacement for Richarlison in the squad, who departed for Tottenham.
Although Richarlison could also play as a winger, Batshuayi will be tasked with duties up front.
The 28-year-old could sign for the Toffees on a loan or permanent deal.