The 13-time England international has slipped down the pecking order at the Etihad Stadium and is heading to Serie A in a loan deal expected to cost 1.25 million euros.
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Richards has been pictured in Florence, joining fellow Englishman and new Roma signing Ashley Cole in Italy, and is expected to undergo a medical ahead of the temporary move later Monday.
Manuel Pellegrini's acquisition of right back Bacary Sagna this summer has seen Richards's opportunities limited, demoting him to third choice behind the Frenchman and Pablo Zabaleta.
West Ham was hopeful of bringing Richards to Upton Park, with Sunderland also retaining interest during the summer, but the versatile defender has opted to move abroad.