Houllier, who is currently technical director of France, left the situation open for a firm offer from Villa chairman Randy Lerner.
Houllier said: 'There are two things you shouldn't say in football - never and always. I don't want to say anything else because if I do.'
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Looking tanned and healthy, Houllier simply gave a Gallic shrug and shook his head when asked about the state of his health.
But former Liverpool manager Phil Thompson - a close ally of Houllierin the past - pushed the Frenchman's cause.
He said: 'Have you seen him? He looks extremely fit and what he wouldbring to Aston Villa is a wealth of experience and organisational ability in the role.
'You see what he did for the golden generation of French football - not the latest group of French players, those who came before.'
Houllier refused to be drawn on whether or not he would be prepared to work with caretaker Villa manager Kevin MacDonald.
But it is understood that there would be no problem with MacDonald continuing at Villa Park.
Meanwhile Carragher, enjoying his big day at Anfield, almost let the secret out when asked about Houllier's imminent return to English football.
'Yes, I've heard that,' he said. 'And I am very grateful that he was able to make it for the match today.'
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