The 30-year-old joined City for £13.8m from Celta Vigo last summer and made 30 appearances, scoring six times.
Half of those goals came in his first three games. He did not start a league game - or score a goal - in 2017.
Last month he claimed his "daughter's face has changed colour" because of the English weather.
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Sevilla have signed Spain forward Nolito from Manchester City on a three-year contract for an undisclosed fee, reported to be £7.9m.