The Australia international midfielder joined on a free transfer from AZ Alkmaar a year ago and played 27 times in Villa's Premier League campaign last season.
However, Al Nasr have expressed their interest in the 29-year-old, who is now expected to finalise a move to the United Arab Emirates club.
A statement on Villa's official website read: "The club can confirm that Brett Holman's contract has been terminated by mutual consent."
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