Chelsea were strongly linked with a move for the 18-year-old towards the end of 2016, while Tottenham Hotspur and Everton have previously been credited with an interest in a player that will be out of contract this summer.
According to The Mirror, however, Man City now lead the race for the teenage full-back, who is said to be keen on seeking pastures new when his Barcelona contract expires at the end of the 2016-17 campaign.
Cucurella spent six seasons in Espanyol's youth set-up before joining Barcelona in the summer of 2012. His Barcelona B debut came at home to CE L'Hospitalet on November 26, 2016.
The left-back has also previously represented Spain at both Under-16 and Under-17 level.