Mutch, part of England's Under 20 squad for next week's friendly against France, is out of contract in six months.
League debut: Birmingham City's Jordon Mutch (right) challenges United defender Chris Smalling
He was a protege of Westley's, and despite lengthy contract talks with Birmingham boss Alex McLeish, no new deal has been agreed.
Mutch, 19, made a big impact on loan at Watford earlier this season and returned to St Andrew's to make his debut in the Barclays Premier League at Manchester United.
The terms of Westley's departure are still being discussed but he will be in demand, with West Ham, Leeds and Ipswich all likely to be interested.
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