The 23-year-old only joined the Seagulls from Getafe last summer for around £15.4m and penned a five-year deal until June 2026.
Cucurella enjoyed a successful first season in England with Graham Potter's side, making 39 appearances across all competitions and was voted the club's Player of the Year.
The Spaniard's impressive performances are believed to have caught the eye of Citizens boss Pep Guardiola, who has identified the Catalan defender as his primary target for the remainder of the summer window.
Despite one report claiming that City are set to accelerate their pursuit of Cucurella, Brighton chairman Tony Bloom has insisted that the club have not received any offers for the left-back.
According to The Athletic, the Seagulls are now in talks with Cucurella over improving the terms of his contract and conversations with the player's representatives are at a preliminary stage.
Brighton allegedly value Cucurella between £45m and £50m, a similar fee which they received from Arsenal when they sold defender Ben White last summer.