Houllier, 63, left Anfield six years ago and has been employed as technical director at the French Football Federation since parting company with Lyon in 2007.
But he has been interviewed by Villa owner Randy Lerner and created a favourable impression with the American multi-millionaire.
If Lerner decides Houllier is the right man to succeed O'Neill, then Villa hope to make an appointment early next week - certainly before their next match at Stoke on September 13.
Houllier enjoyed considerable success with the Reds and led them to a UEFA Cup, FA Cup and League Cup treble in 2001.
Villa sources believe he has the reputation and CV to keep Villa on an upward curve after three successive top six finishes in the Premier League.
Before he moved to Liverpool, he also enjoyed title success with Paris St Germain and spent a decade overseeing the development of French football.
Former West Ham boss Alan Curbishley and caretaker boss Kevin MacDonald have also been interviewed for the post by Lerner and Villa chief executive Paul Faulkner.