Anfield legend Thompson was Houllier's number two during his six-year stint as Reds' boss and the Frenchman was keen on rekindling the partnership in his new role as Martin O'Neill's successor at Villa Park.
But Thompson has decided to reject the "flattering" offer and will remain in his role as a Sky Sports pundit.
"Had circumstances been different, I would have been delighted to accept the chance to work with Gerard Houllier once again at Aston Villa," he said.
"But I had to weigh up the pros and cons and while it was hugely flattering and enticing to be asked, I had no choice but to turn the offer down.
"With Gerard, you are signing up to 12-hour days, you have to be totally committed.
"I would throw myself at such a challenge but at the same time I do not want to uproot my wife and two boys and I'm not someone who could live away from them through the week."
Houllier, 63, has been out of work since leaving Lyon in 2007 and returns to English football six years after his Anfield exit.
He will be unveiled to the media on Friday and will take charge of his first game on Monday against Stoke.