The Senegal defender, a £2.5m buy from Newcastle, has made just five Premier League appearances and has fallen behind in the pecking order.
Unsettled: Beye, who spent two season at St James' Park has struggled at Villa
Sunderland manager Steve Bruce tried to sign Beye during the January transfer window but had a £1.5m bid rejected.
But it is now almost certain the unsettled defender will quit Villa Park in the summer.
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