The full-back arrived at the Amex from Spanish side Getafe last summer, and had a stellar first season in the Premier League.
Cucurella has four years remaining on his current deal at Brighton but his future is under the scanner as top flight champions Manchester City have made him one of their priority targets this summer.
The Seagulls are yet to receive any bids for Cucurella and although they want to keep him, they are realistic about their chances of holding on to him if a top club come calling with a big offer.
Brighton are tipped to be valuing the full-back at a whopping £50m but ideally would want to have him in their ranks beyond this summer.
And Graham Potter’s side have started preliminary negotiations with Cucurella’s agents over a new contract for the player.
Although Brighton are aware of Manchester City’s interest in Cucurella, they are looking to hand him a deal on fresh terms as a reward for his performances last season.
It remains to be seen whether Manchester City will approach Brighton with an official bid for the Spaniard in the ongoing window.
