The Blues have missed out on a number of defensive signings this summer, losing out on key targets Jules Kounde, Matthijs de Ligt, Nathan Ake and Presnel Kimpembe.
It was reported a fee of £52.5million had been agreed between both clubs for the Spanish left-back.
However, in a statement Brighton said no agreement was in place at present.
It read: "Contrary to inaccurate reports from numerous media outlets this evening, no agreement has been reached with any club to sell Marc Cucurella."
Chelsea defender Levi Colwill is expected to go the other way, however, this is expected to be in a separate deal.
Cucurella looked set for a move to Manchester City and handed in a transfer request in an attempt to force the move through.
However, the deal stalled over Brighton's asking price, with City unwilling to pay £50m for a player with only one year's experience of Premier League football.
It's understood City's offer of £35m and their approach to negotiations didn't go down well with the south coast club too.
This allowed Chelsea to swoop in, however, it's not clear whether they will get the deal sewn up.
Chelsea have been very busy in the summer despite the numerous setbacks in the transfer window, recruiting the likes of Raheem Sterling and Kalidou Koulibaly.
They're also set to announce the signing of England youth star Carney Chukwuemeka, Chelsea understood to be paying up to £20m for his services.
Thomas Tuchel is also understood to be keen on bringing Leicester centre-back Wesley Fofana in too.
The Premier League is back and talkSPORT has it covered, with games on Friday, Saturday and Monday, beginning with Crystal Palace vs Arsenal on 5 August