Amankwah joined City in 2016 and after impressing for the club’s EDS Squad, the 20-year-old then signed a new contract at the Etihad Stadium in October 2019.
The London-born defender made two loan appearances for Rochdale last season, but his move was cut short due to injury.
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Manager John Coleman said: “Yeboah has been blighted a little bit by injuries, but he’s a talent and hopefully we can get him going.