Poveda, 15, is currently on loan at Championship side Brentford but City are confident of striking a deal to incorporate the talented wideman into their youth ranks.
The diminutive winger has received several call-ups to England's Under-16 side in recent months.
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His skills against Japan U16s went viral last October, with the video posted from his Twitter account re-tweeted over 1000 times.
The youngster has played in the same England ranks as City prospect Jadon Sancho, who is highly thought of at the Etihad Stadium.
Brentford had been hopeful of keeping hold of Poveda, but City are thought to be close to agreeing a deal with Barca.
The news comes as it is reported that Brentford are set to close their academy, three years after it was opened.