Everton is among several teams interested in signing the Belgian forward before the January transfer window closes, according to Chris Bascombe of The Telegraph.
The Toffees weren't expected to conduct much business this month but it's understood they will explore the possibility of signing Batshuayi once his loan spell in Spain ends.
Batshuayi's time with Valencia is expected to end in the coming days once negotiations over his exit are completed, according to club sporting director Mateu Alemany.
The looming withdrawal is understood to be the result of Batshuayi's deteriorating relationship with Valencia manager Marcelino, who publicly criticized the 25-year-old after removing him at half-time of a Copa del Ray match because of his poor performance.
Batshuayi joined Chelsea from Marseille in 2016 for a reported £33.2-million fee. The forward struggled to break into the first team during his first season before moving to Borussia Dortmund on loan in January 2018.
After joining Valencia on loan last summer, Batshuayi has managed just one goal in 15 La Liga appearances this term.
Meanwhile, Everton forwards have struggled to produce goals this season; Richarlison has been one of their primary sources up front with nine Premier League goals.