The 23-year-old has made a huge impression at the Amex since his £15.4m move from Spanish club Getafe last August.
The full-back, who has been capped once by Spain, was named Albion Players' Player of the Season and Player of the Season after a series of stellar performances during the 2021-22 campaign.
Cucurella made 35 appearances for the Seagulls, scoring once and providing one assist, and helped the club keep eight clean sheets.
The Spaniard also successfully won 67 per cent of his tackles during his debut season in the Premier League.
Cucurella’s stand out campaign has caught the eye of heavyweights Chelsea, champions Manchester City and Tottenham Hotspur.
And, according to The Sun, the Blues will have to pay £45m to secure the left-back’s services and beat off interest from City and Spurs.
Chelsea are eager to bolster their defensive ranks this summer. The club have confirmed that Antonio Rüdiger and Andreas Christensen will exit Stamford Bridge, while César Azpilicueta is likely to depart.