The England U21 goalkeeper is expected to leave Turf Moor, despite Burnley's return to the Premier League.
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Trafford is the subject of major interest from Newcastle United.
However, talkSPORT says City are now weighing up triggering a buy-back option in his deal.
Trafford left City for Burnley in 2023 for £19m and can be re-signed for a set fee for £40m.