The England attacker signed a six-year deal in November 2018 and is currently happy at the Etihad Stadium but could be open to a move in the future.
For their part, Madrid are very interested in bringing the former Liverpool man to the Santiago Bernabeu and wanted talks with his camp to lay the groundwork for a transfer in the years to come.
Sterling has made a fine start to the season, scoring five goals in his five Premier League appearances this season.
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Nonetheless, we was a surprise omission from the team which beat Watford 8-0 on Saturday, spending the whole game on the bench.
Sterling has won two Premier League titles in his four year stint at City, who bought him in 2015 in a deal worth an initial £44 million.
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