The Spaniard has recently been rewarded for an impressive first year at the Amex Stadium by being given the club's Player Of The Year award for 2021-22.
The 23-year-old, who can play in a number of positions on the left-hand side, made 35 starts in the Premier League, helping the Seagulls finish in ninth position in the standings.
When quizzed on whether he would consider a transfer to Manchester City, Cucurella has acknowledged that he would struggle to turn down a move to a bigger club.
However, according to The Sun, the top-flight champions and Chelsea have been informed that it will cost £45m to secure a deal for the player.
Should a deal come to fruition, Brighton would be trebling the £15.4m that they paid Getafe for Cucurella's signature last summer, and negotiations could take place in the future with each of City and the Blues requiring another option on that side of the pitch.