Houllier's nine-month reign ended by mutual consent because of his recent heart problems which resulted in him not taking charge the final five games of last season.
Everton boss David Moyes, Steve McLaren, Carlo Ancelotti and Mark Hughes are just a few of the names being mentioned as possible replacements.
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Hide AdHoullier, 63, had been hoping to return to his post but has eventually acknowledged he needs to recuperate before a possible return to football.
He said: "I am extremely disappointed that I will not have the opportunity to manage Aston Villa next season.
"My health has improved considerably since I was taken ill on April 20. I now intend to take the next few months to concentrate on recuperating fully before I may return to football.
"I was very much looking forward to the prospect of my first full season as Villa manager and returning for pre-season training to prepare for the campaign ahead, a luxury that I did not have last season."