And with Madrid having a major clear out this summer to raise funds, Reguilon could be allowed to leave.
Madrid rate Reguilon highly, but have Ferland Mendy and Marcelo already for the left-back position.
Sky Sports reported last week that Everton had made an £18m (€20m) bid for Reguilon.
The Toffees will be dismayed to learn of competition from Chelsea, who are spending heavily this summer.
Chelsea are expected to make a bid in the coming days that will improve on Everton’s offer.
Frank Lampard is in the market for a left-back with Leicester and England’s Ben Chilwell top of his list.
However, Chilwell’s £80m (€88.9m) price-tag has Chelsea looking at other options, including Reguilon.
Sevilla would like to keep Reguilon for another year, but his performances this season have alerted many clubs.
Reguilon made 33 appearances in the 2019-20 campaign for Sevilla, scoring two goals and assisting four.
A homegrown, Madrid-born talent, Reguilon joined Real’s academy at the age of eight. He appeared 22 times for Madrid before his loan move to Sevilla.