According to Birmingham Mail, The Lions have decided not to extend the winger's contract which expires during the English summer.
Instead, the club is eyeing other names to strengthen their squad ahead of their Premier League season.
Defenders Alan Hutton and Tommy Elphick will reportedly join Adomah through the exit door.
The Ghanaian sensationally left Middlesbrough after Matchday Two in the Premier League in 2016 following their promotion from the second tier.
He played for Bristol City in the Championship between 2010 and 2013 and Barnet in League Two between 2008 and 2010.
In the recently ended season, the 31-year-old made 39 Championship appearances for Villa, started 24 of the games and scored four times. He scored 10 goals less than the previous campaign when he finished the term as the club's top scorer and Player of the Season.
The winger was part of Ghana's squads for the 2013 Africa Cup of Nations and the 2014 Fifa World Cup but was snubbed for next month's continental showpiece in Egypt where the Black Stars have been drawn against Cameroon, Benin and Guinea-Bissau in Group F.