The Citizens, who won the treble last season and are on course for a domestic double, made a bid for the 16-year-old.
However, Relevo in Spain indicates that Dura was not interested in moving to England.
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He may believe that he can get a move to a top club in Spain in one or two years instead.
The likes of Real Madrid, Barcelona, and other top clubs in Europe are all interested.
City were hoping to secure a quick deal, but Dura will stay with Valencia for the time being.