The relegated Premiership club have been tracking the 19-year-old speed merchant, who broke into the Bluebirds senior set-up this season.
Jerome was the clubs' top marksman with 20 goals and also made his international debut with Peter Taylor's England Under-21s, winning three caps.
The Echo understands that the St Andrews club have contacted the Bluebirds with a cash deal of £1.5m, plus a further £1.5m in add-ons such for appearances and goals.
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