Newcastle have enquired, but Hart favours a move to West Ham.
Regular first-team football would be a major boost for Hart, whose City contract expires in 2019, as he bids to secure his position as England's No1 for the World Cup in Russian Federation in 12 months' time.
Hart is due in London on Monday for a medical.
Winston Reid is still recovering from a knee problem and will miss a pre-season game for West Ham.
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But Hart, who has won 71 global caps since 2008, has continued to England's first choice despite his exile in Italy.
The deal will be on an initial season long loan, which will eventually lead to the 30-year-old joining the Hammers in a permanent £10m deal next summer. "It's not nailed-on mine, it's no one's".
"It's another exciting adventure, another move, the next step in my career, the next challenge for me personally".
West Ham have already signed Argentina defender Pablo Zabaleta from Manchester City.
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