Ashley has so far invested around £280million in the club that he bough back in May 2007.
Llambias said: “Mike Ashley has no intention of putting the club up for sale. He is still extremely passionate about strengthening the club and making it a real success.
“We are balancing the books and getting the finances in order, but there’s more work to be done and he’s committed to doing that for the long term.
“That said, it’s worth going back to the analogy of the house that’s not for sale. If suddenly an incredible offer comes in, he may have to consider it.
“From time to time we are approached by people claiming to have an interest in buying the club. Our message to them is clear: buy a box for a commitment of five seasons and then we will know you are serious. No-one’s taken us up on that offer.”
Llambias insists the Magpies will not be making any big-money signings in the future.
He said: “The days of Newcastle United acquiring ‘trophy’ signings who command huge salaries for past successes on the pitch are over.
“Yes, they have generated excitement and anticipation in the past, but ultimately many of them have left the club poorer and with little to show for it in terms of our standing in the league.”