The fee could rise to £19m with add-ons for the 20-year-old, who is currently on international duty with England at the European Under-21 Championship.
Trafford, who is yet to appear in the Premier League, has spent the previous two seasons on loan in League One with Accrington and Bolton.
Burnley face champions City in their top-flight opener on 11 August.
City have included a buy-back option into the deal for Trafford, who now has to complete a medical and agree personal terms with the Clarets.
More to follow…
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