The 23-year-old starred on loan for Sevilla this season, helping Los Rojiblancos finish in fourth-place.
Real are happy to sell the Spaniard in order to raise funds as they have Ferland Mendy as their starting left-back.
Everton lodged an £18m offer with Los Blancos last week.
Reguilon is viewed as a far cheaper alternative to Frank Lampard's number one target - Ben Chilwell.
Although Leicester have softened on their £80m asking price, it would still cost more than Chelsea want to spend on the England international.