The Liverpool great was hired last November in a Premier League return that many expected would eventually lead to the manager's role back at Liverpool, where he played 710 matches — many as captain — and is widely regarded as one of its best players.
The 42-year-old Gerrard joined Villa after a three-and-a-half year stint in Scottish football where as a first-time head coach he transformed the fortunes of Rangers and ended the long-time dominance of Glasgow rival Celtic.
Villa finished in 14th place last season.
The former England midfielder played 17 seasons for Liverpool and retired as a player in 2016 after one-and-a-half seasons with the LA Galaxy of Major League Soccer.