The news could spark a bidding war for the 28-year-old, who is almost certain to leave the Nou Camp after falling behind Lionel Messi, Neymar and Luis Suarez in the pecking order.
City director Txiki Begiristain is a former official of the Catalan club and is understood to retain close connections with Barca.
And reports suggest he will launch an official approach in the coming days.
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Pedro could become the subject of a bidding war between Manchester United and Manchester City
It is believed they have become increasingly frustrated in their pursuit of Wolfsburg star Kevin De Bruyne.
While a bid of around £50m is thought to be in the offing, the German club are reluctant to sell and Pedro could be seen as an alternative.
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