Young has 20 months left of the four-year contract he signed in 2008 and has shelved talks on any possible extension until the end of the current campaign.
That would leave him with only 12 months to run and he could leave for nothing in 2012 if he opts not to sign on the dotted line.
But Houllier does not want to sell Young and revealed running down the contract is a possibility should no new deal be tied up with the England winger.
Houllier said: "The club is protected until 2012. He is not at the end of his contract this season.
"If he is four years on his contract, and he wants to leave next year, then it's the same.
"To me, the main thing is we have shown that we want to keep him, we like the boy, I think he likes the place where he is.
"He probably knows that he will improve so it is just a matter of time whether he signs now or the end of the season.
"Obviously at the end of the season something is going to have to come out."
Houllier added: "It is not a matter of selling Ashley. We don't want to sell him, we want to keep him.
"Maybe we will keep him until the end of his contract. Is that a possibility? Yes."
Houllier was also asked whether he thought Young, who has been closely linked with a move to Tottenham may have been tapped up.
There have also been reports the former Watford player wants a get-out clause in any possible new deal.
Houllier said: "Could Young have been tapped up? "You never know in football.
"I've read that Tottenham are after him and that he is after a clause. He has no clause anyway."
Houllier believes the most important factor for Young at this juncture is to continue to improve his game.
He has impressed in the new 'hole' role given him by Houllier and earned his first competitive start for England in last week's Euro 2012 qualifier with Montenegro at Wembley.
Houllier said: "I think it is true when Ashley said he wants to concentrate on his football.
"I spoke to him and said 'the main target for you is to improve, to step up a level.
"To do that you can't lose two months or three months talking. He said 'okay, at the end of the season we will sit and talk.'
"That is fine, I am happy with that."