According to ESPN, Frank Lampard’s side has emerged favourite to sign the 23-year-old ahead of Premier League rivals, Manchester United and Tottenham Hotspur.
Chelsea now sees the defender as their number one target after they failed to reach an agreement with Leicester City for their left-back, Ben Chilwell.
Discussions are ongoing between Chelsea and Real Madrid as to whether the deal for the Spaniard would be a loan move or a purchase for a fee of around €25 million.
Reguilon spent this season on loan at Sevilla from Madrid.
He broke into the Los Blancos first team in the 2018-19 season with Santiago Solari as a coach, replacing the veteran left-back, Marcelo in the starting XI.
However, when coach Zinedine Zidane requested the signing of defender, Ferland Mendy, from Lyon in the same position last summer, the decision was taken to send Reguilon to Sevilla on loan.