Curbishley, out of football since ending his spell as Hammers gaffer two years ago, is understood to have been interviewed by Villa on Wednesday.
He joins reserve-team coach Kevin MacDonald, who formally applied for the job on Tuesday after a spell as caretaker manager, in being in contention for the Villa Park post.
Curbishley carved out his managerial reputation in establishing Charlton as a top-flight club.
That would fit Villa's criteria of wanting a manager with Premier League experience, although this has not ruled MacDonald out of the equation.
Curbishley won a case of constructive dismissal against West Ham after parting company when several players were sold without his permission.
The 52-year-old joined Villa as a player from Birmingham in 1983 and made 36 appearances for the club.
Villa are to speak to other potential candidates before making an appointment, which they hope will come before the next match at Stoke after the international break.
Ronald Koeman has also made it public that he would be interested in the role - but speculation linking Mark Hughes and David Moyes to Villa is wide of the mark.