Villa are drawing up a shortlist, also likely to include Fulham's Mark Hughes and Everton's David Moyes, after Houllier's nine-month reign ended because of concerns over his health.
They are hoping to appoint Houllier's successor before the end of June to give him time to assess the current squad and bring in new signings prior to the 2011-12 campaign. There has been intense speculation that Hughes is bound for Villa Park and he is the current favourite with the bookmakers.
He signed a two-year deal last summer although he can activate a get-out clause for the final 12 months.
But Ancelotti is also understood to be impressing Lerner given his outstanding track record. He led the Blues to the double in his first season at Stamford Bridge before being sacked by Chelsea last month having ended the season trophyless.
Lerner would have to convince Ancelotti that Villa match his own ambitions and can mount a serious challenge for Champions League football.
Villa may also find Ancelotti's wage demands could be a stumbling block after reportedly earning around ?£5million last season at Chelsea.
He has been linked with a move to newly-promoted QPR should they dispense with Neil Warnock.
Ultimately, Hughes may turn out to be a more realistic proposition for Villa should he decide to seek fresh pastures.
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Source: PA