The Daily Star Sunday says United boss David Moyes, who takes his side to the Etihad today for the Manchester derby, has been trying to sign a playmaker.
And City already have close links to Iniesta through Sporting Director Txiki Begiristain and CEO Ferran Soriano - who were with him at Barcelona.
The Barcelona superstar is understood to be disappointed with the new terms he has been offered at the Nou Camp.
That is despite the fact Barca have placed a double-your-money deal on the table of £200,000-a-week.
Iniesta believes he should be the second-highest paid player at the club after Lionel Messi. And while he is now 29, Iniesta remains one of the outstanding players in the world.