Estadio Deportivo says City are planning to cash in on Couto, who spent the past season at FC Girona.
The 21-year-old right-back is to be sold, with City demanding 40 million euros.
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If no interested party is willing to pay this sum, City will, according to the report, sell Couto to Girona - probably for a lower price, after all, both clubs belong to the City Football Group.
Bayer Leverkusen, among others, have signaled interest in the Brazilian, who may need to find a successor for Jeremie Frimpong.