The 23-year-old midfielder was key to Rotherham winning promotion to the Championship last season.
LancsLive reports that Wiles fits the profile sought after by Vincent Kompany and chairman Alan Pace.
Burnley, who have been relegated to the Championship, announced the signing of MK Dons star Scott Twine on Sunday.
Wiles made 53 appearances and scored five times for Rotherham last season.
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