The Daily Mail reports that Barry is ready to take a pay cut in order to ensure that the loan move goes through.
Barry has long been linked with a move away from City after having fallen down the pecking order at Eastlands.
Everton are also holding talks with Wigan over a deal for James McCarthy.
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.