The England under-21 goalkeeper joined City from Burnley over the summer with the hopes of being their new number one. However, the arrival of Gianluigi Donnarumma from PSG ended those plans.
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 that 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.