The sportswear magnate has twice unsuccessfully tried to offload the business he bought for £134.4million back in May 2007, but has since embarked upon a blueprint to make it self-sufficient, a policy which has not gone down well with his critics.
Supporters who expected the £35million the Magpies raked in when they sold Andy Carroll to Liverpool in January to be invested in marquee signings this summer have been disappointed, and the strained relationship with the hierarchy has grown ever more toxic.
However, answering fans' questions submitted by the city's evening newspaper, the Evening Chronicle, Llambias revealed that Ashley, who has invested a total of around £280million in the club, has no plans to sell up.
He 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 plenty 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."
However, Llambias also hinted that the anger which has been directed at the regime has done little to encourage Ashley to pour more cash into Newcastle.
He said: "Criticism is part and parcel of the job, abuse is not. This makes life uncomfortable and certainly doesn't make Mike feel more inclined to put his hand once again in his pocket.
"That's not stubbornness, it's human nature. I think most of us would feel exactly the same."
Much of the ire from supporters surrounds the club's summer recruitment policy, which saw Kevin Nolan, Jose Enrique and Joey Barton leave after failing to agree new contracts and seven new signings arrive, but not the striker on whom both manager Alan Pardew and the Toon Army had set their hearts.
Llambias said: "It was everyone's desire at the club to bring in a striker. We worked hard to make that happen, but ultimately
couldn't complete a deal that we had hoped to."
Asked further where the Carroll money had gone, Llambias replied: "We made it clear when we sold Andy that the fee we received would stay in the club, and it has.
"The money will be spent prudently within the club and on new players as and when we are in a position to do so. We didn't promise to spend all the money in this window.
"Money will be available going forward, for the right player at the right time. If the club had been able to move on other transfer targets this summer, then more money would have been spent."
However, Llambias, who revealed that wages will account for around 65 per cent of turnover this season, seven per cent up on last season, confirmed that the days when the Magpies could sign players like Alan Shearer and Michael Owen are over.
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."