David Moyes is looking for a long-term successor to Sylvain Distin and he has reportedly been captivated by the Dutch international.
Having had the player watched on a number of occasions this term, the Toffees are ready to step up their interest in the highly rated centre-back.
According to Liverpool Echo, Everton officials are hoping an offer in the region of £6 million would prove sufficient.
De Vrij, 21, has already made 100 Eredivisie appearances for the Dutch giants and he is widely regarded as one of the most talented defenders in world football.
He has broken into the Netherlands set-up under Louis van Gaal and started two 2014 World Cup qualifiers for Oranje.
As much as Feyenoord chiefs would like to keep hold of their prized asset, they might not be able to resist a lucrative offer from England.