New Blues boss Marco Silva is looking to add to his squad ahead of the new season having made a low-key start to life at Goodison Park.
Silva replaced Sam Allardyce as manager last month, but is yet to make a first-team signing with new director of football Marcel Brands leading the recruitment drive.
Brands is aware of the need to trim the Blues’ squad, with as many as eight players likely to leave before the transfer window closes next month. Silva, though, is keen to add at least four new faces as he prepares for his first season in charge on Merseyside.
Zaha would be seen as a marquee signing, and one which would likely threaten Everton’s transfer record, the £45 million ($51m) capture of Gylfi Sigurdsson from Swansea last summer.
The Ivory Coast winger is understood to be open to the idea of leaving Palace, who would demand around £50m ($65m). Everton, though, believe they would face strong competition from the likes of Tottenham, Borussia Dortmund and even Liverpool if they were to open negotiations. Zaha scored nine times for the Eagles last season, equalling his best ever campaign as a professional.