The 19-year-old has made the breakthrough into the first team at Camp Nou this season, featuring on six occasions in all competitions, including five outings in La Liga.
Gonzalez has a contract at Camp Nou until June 2024, but Barcelona's financial problems has placed them in a difficult position when it comes to improving the deals of their highly-rated youngsters.
The report claims that the Citizens want to sign a new central midfielder next year, as Fernandinho prepares to leave the club on a free transfer.
Gonzalez featured on 27 occasions for Barcelona B before making the breakthrough into the first team, and he played 45 minutes of Saturday's La Liga clash with Atletico Madrid at Wanda Metropolitano. body check tags ::