The England U21 goalkeeper joined City from Burnley over the summer with the hopes of being their new No1. However, the arrival of Gigio Donnarumma from PSG ended those plans.
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The Manchester Evening News says Trafford's departure now appears "inevitable" as he wants senior football at this stage in his career.
It's been suggested Trafford could make a transfer demand in the New Year over concerns regarding his England World Cup hopes.
Among clubs watching developments are West Ham United.