The Spaniard only arrived on the South Coast last summer after Brighton signed Cucurella from Getafe for a £15.4m fee.
However, with Oleksandr Zinchenko potentially making a move to the English capital to join Arsenal, Cucurella could be targeted by the Premier League champions as the Ukrainian's replacement.
According to The Sun, Man City are set to step up their efforts to sign the left-back this summer, although Brighton's asking price could prove to be a stumbling block.
The Seagulls are reportedly looking to secure a fee in the region of £50m for the 23-year-old, but City are keen to bring that price down.
With Cucurella linked with a move away from the Amex Stadium, Brighton are looking to enter talks over an improved contract for the Spain international.