Zirkzee made a name for himself in his homeland last season by scoring 33 goals in 27 games last season for the Feyenoord youth team.
It is well known that Everton are looking to boslter their youth ranks this summer, with the 'Toffees' having already brought in QPR winger Joss Bowler and the club also believed to be in advanced talks with Newcastle over midfielder Lewis Gibson.
Everton's head of recruitment Steve Walsh is clearly casting the net far and wide as he looks to build for the future, with 16-year-olds Zirkzee and Gibson both considered to be among the most talented players of their age group in their respective countries.
Should the pair make the move to Merseyside, they will look to emulate Domini Calvert-Lewin and Ademola Lookman, who made 18 appearances between them in the league last season, despite many seeing them as signings for the future.