The Daily Mail says the Hammers are eyeing the England international, 25, as they look to strengthen their squad over the summer.
Richards has been offered a contract extension at City.
However, the Birmingham-born right back has shown a reluctance to sign on the dotted line given his lack of playing time this season.
Richards is also an £8million summer target for ambitious Hull City.
Last month, he hinted he could quit the Etihad after 11 years.
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