The £50m asking price for the Manchester City target is not a problem for the Blues.
The Spaniard handed in a transfer request on Friday in a bid to push through a move to City but the premier league champion will not pay the asking price.
The Seagulls had previously turned down a £30m bid for the full-back from the club.
Cucurella, who joined from Getafe in a deal worth around 15 million pounds, was named the player of the season for the Seagulls.
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Cucurella has four years left on his contract at the Amex and it would take a lot of money to let him go. The left-back asked to be sold.
With doubts surrounding the future of Marcos Alonso, Barcelona are said to be interested in signing the left-back. Cesar Azpilicueta has one year left on his contract and the Spanish giants want him.
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Ben Chilwell missed the majority of last season with a knee injury but has returned to full fitness.
The side has made two signings this summer, the first being the signing of Manchester City's Raheem Sterling for over fifty million dollars and the second being the signing of Kalidou Koulibaly for over thirty million dollars.
Sky in Italy says that Napoli are in talks with the Blues about Kepa Arrizabalaga.
The west London club have indicated they will pay three-quarters of his salary, with discussions centring around a number of bonuses.
Intermediaries involved in the deal are trying to find a way to get Napoli to pay.
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Kepa was the world's most expensive goalkeeper when he was signed by the Blues in August of last year.
He made just four appearances in the league last season as the club's second choice behind Mendy.
The transfer window will close at 11pm on September 1st.
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