The teen is regarded among the most talented youngsters at La Masia and Barca know he is being monitored by clubs across Europe.
El Mundo Deportivo says Barca are particularly nervous about City's interest after it emerged an offer has been made to Nico's father, Fran Gonzalez, to join Pep Guardiola's backroom team.
A former Spain international, Fran made over 600 appearances for Deportivo La Coruna.
City have already put one over Barca in the past 18 months, landing wonderkid Brahim Diaz from Malaga ahead of the Catalans - a deal which is stilled rued by Barca chiefs.
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