The Donegal-born singer, who has amassed a legion of fans throughout the Emerald Isle, was quoted in the Sunday People as saying: "I'm leaving Ireland."
But when the 44-year-old was asked by the BBC if he intended to head for pastures new, he simply responded: "No, I'm afraid not."
The easy-listening star, who has an MBE for his services to music, stressed that his heart remains in the west coast of Ireland.
"It's amazing, really, these things can be written without any grain of truth at all. It's ridiculous. I don't know why newspapers write these things. I don't know how they continue to get away with it. It's pointless," he said.
"We do intend, in the near future, to sell the house we are living in, or put it up for sale.
"But we didn't feel there was any need to make a big announcement about that, because we are only selling it to build a smaller house. That's the sum total of the whole story."
From humble beginnings as a teenager on the Irish country music scene, O'Donnell has amassed a fortune over the years, as well as a world-wide fan-base.
Until his marriage to wife, Majella, in 2002 he lived with his mother in the Donegal village of Kincasslagh and regularly hosted tea parties for thousands of fans - many of whom were in their 60s and 70s.
He has a second home in Tenerife but his main home is still at Cruit Island near Kincasslagh, where he also owns the Viking House Hotel.
O'Donnell makes no secret of his deep affection for his native home in songs such as Home to Donegal and My Donegal Shore.
He says his only move in the near future will be out of his current six-bedroomed house, which has been recently renovated, and into a smaller home.
"It really is too big... for us. We just decided we would put it on the market to see if there would be any interest. Our intention is to build, or even buy, another house, a smaller house, at home.
"The reality of it is that we're living in Donegal and we will be living in Donegal. If we go to Tenerife for a period in the winter time, I still am living in Donegal. How many other people chose to go away and spend winter months in warmer places?
"Over the years, since I started touring, I have probably spent less time at home than anybody that lives in Ireland. But I always feel I am living at home.
"My roots are in Donegal and that's where I feel that my home is."
So in the words of one of his more famous songs: "My heart will lead me back home to my Donegal." And that is where he intends to stay.
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