The 23-year-old has been a standout performer for the Seagulls this season and his form has been recognised as he was named the club's Player of the Season earlier this month.
According to the Daily Mail, Pep Guardiola is keen to bring Cucurella to the Etihad Stadium this summer, with the Citizens in the market for a new left-back.
In the absence of Benjamin Mendy, who is serving a club suspension, Joao Cancelo has starred at left-back this term, featuring in this position on 31 occasions across all competitions.
Oleksandr Zinchenko has also performed well on the left side of defence when called upon, but nevertheless, City intend to bolster their options at left-back and have identified Cucurella as a potential target.
The Spaniard's age and versatility on the left flank are believed to be two characteristics which have 'convinced' City to move for the defender this summer.
Cucurella, who joined Brighton from Getafe for around £15.4m last summer, is under contract at the Amex Stadium until June 2026.