The 17-year-old has caught the eye of several top clubs across Europe and City are keeping tabs on the talented Spaniard.
According to El Nacional, Gavi has a £42million release clause in his current deal with the Catalan giants, which runs until the summer of 2023.
Cash-strapped Barcelona could be forced into selling him if a suitable offer is made or his release clause is met, helping make a small dent in their huge £1bn debt.
And City could be the club to make a move for Gavi who has since broken into the Barcelona first team in the past year.
After being snapped up by Barcelona’s academy in 2015 when he was just 11, he went on to sign his first professional contract with the club in September 2020 before being promoted to the first team the following year.
He is said to be highly-regarded by Xavi, who has handed him plenty of minutes since taking the job in November.
Pep Guardiola would be keen to bring Gavi to the Etihad but reports suggest the youngster would be ‘hesitant’ about making such a big move so early on in his career.
Gavi is also reportedly excited about the prospect of playing alongside the likes of Pedri and Ansu Fati – two of the clubs other very promising youngsters.
Gavi has made 22 senior appearances for Barcelona this season, scoring once and setting up his team-mates to score on three separate occasions.