The 23-year-old enjoyed an impressive first season with the Seagulls, after arriving from Getafe last summer for around £15.4m, and he was named the club's 2021-22 Player of the Season.
According to The Guardian, Pep Guardiola is determined to sign his Spanish compatriot, who has been identified as City's primary left-back target this summer.
The report adds that the Premier League champions are preparing to submit their first bid for Cucurella - who could cost in the region of £45m - and hold advanced talks with Brighton in the coming days.
Graham Potter's side are understood to have already lined up a replacement for Cucurella, as they have identified Porto left-back Zaidu Sanusi as their preferred target should the Spaniard move to the Etihad Stadium this summer.
City have already completed the signings of Erling Braut Haaland and Julian Alvarez, the former of whom competing his move earlier this week, while Leeds United midfielder Kalvin Phillips is also believed to be on their radar as they look to replace Fernandinho.