Rangers are reportedly set to sign defender Joleon Lescott.
Southampton selected the Scot as their new assistant manager, working alongside Claude Puel.
The caretaker manager took charge of the final seven matches of Villa's horror season.
Bevington becomes the latest advisor to head out of Villa.
Aston Villa have taken just one point from the seven matches that Eric Black has had at the helm.
The Villans' dismal season ended in a 4-0 defeat at the Emirates.
Aston Villa are set to play in the Championship next season.
The Scot was placed in caretaker charge of the club in late March following Remi Garde's departure.
Relegated Villa say goodbye to the Premier League on Sunday afternoon when they face Arsenal at the Emirates Stadium.
The youngster has barely featured for Aston Villa this season.