The Londoners offered more than £ 50 million for the 24-year-old Spaniard on Tuesday, which is the amount the seagulls are demanding for Cucurella.
Brighton has not yet given an official response to the offer, insider Fabrizio Romano reports.
Earlier it was reported that Chelsea had already agreed to a contract with the player.
Levi Colwill’s move from Chelsea to Brighton has also been discussed during talks between the clubs. If the sides agree, the deal for the 19-year-old defender will be formalized as a separate transfer.
Colwill played for Huddersfield on loan last season.