The 23-year-old France left-back had been suffering with a thigh injury since his summer move from Monaco.
He missed City's opening 2-0 Premier League victory over Brighton on Saturday.
However, he took part in a training session in Spain on Monday and could be available for their home match against Everton next Monday.
City are in Catalonia for a warm-weather training camp that will include a friendly against newly promoted La Liga side Girona.
Mendy, who became the world's most expensive defender when he joined City, was carrying the injury when he signed.
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