Mings was on loan at the Villa Park club for the second half of this season.
He helped the team achieve promotion to the Premier League through the playoffs.
According to Sky Sports News, Villa want to sign him in time for next season.
It is unclear if it would be another loan deal or a permanent transfer.
The source also claims that Cherries manager Eddie Howe would be willing to let him leave for the right price, with Mings also keen on the move.