Fabrizio Romano claims that as the Blues near a deal for Cucurella, Chelsea and the defender have reached a personal understanding.
Brighton has rejected repeated offers from Manchester City, Chelsea's Premier League opponent, and Pep Guardiola's team is refusing to pay Brighton's £50 million asking price for Cucurella.
The Blues have already achieved a major victory after reaching a personal agreement with Curerella to transfer to Stamford Bridge.
Cucurella is now prepared to join Thomas Tuchel's squad as soon as the club and Brighton can agree on a transfer cost.
The 24-year-old put in a transfer request last week to push through a deal because he was determined to join Manchester City this summer.
But as the west London club looks to strengthen their defence ahead of the new season, Chelsea is currently in the lead to recruit the Spain star.