The 24-year old is a former graduate of West Brom's academy and has been impressing in the Scottish Premiership this season making 28 appearances overall.
Burnley in particular have been scouring the market for a defender and, with their budget limited, a bargain deal for Birmingham-born Fitzwater could suit.
Livingston are likely to demand around £1million for the 6ft 3ins defender who has had to shoulder responsibility in a relatively young side.
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