The Daily Star says City are set to cash in on Barry when he completes his 'free transfer' to Everton.
The veteran midfielder, 33, is out of contract at City this summer and became a free agent this week.
Under the terms of his loan move to Everton last season means City will actually receive £1m if Barry signs a 12-month deal at Goodison Park, with an extra £500,000 for every additional year he stays at the club.
Barry was exceptional last term at Goodison Park with Arsenal, Stoke and QPR all interested in the free agent.
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