The 23-year-old has allegedly been identified by Pep Guardiola as his primary left-back target this summer, with one report claiming that the Citizens are poised to make an offer for the Spaniard.
According to The Argus, one of Cucurella's representatives flew from Madrid to Manchester last week ahead of holding talks with Man City's director of football Txiki Begiristain.
The report adds that Brighton are expecting to receive an offer from the Premier League champions, although a formal bid is yet to have been made.
Cucurella only joined the Seagulls last summer from Getafe for around £15.4m, but he has previously admitted that he would find it difficult to turn down a move to the Etihad Stadium.
The Catalan defender, who still has four years remaining on his contract, made 38 appearances for Graham Potter's side across all competitions in the 2021-22 campaign, and he was voted as the club's Player of the Season.
Man City are also looking to sign Leeds United midfielder Kalvin Phillips, who has allegedly told the Whites that he wants to join Guardiola's side this summer.