The X Factor finalist, who released her debut album Mine & Yours this week, insisted that the brief relationship didn't mean anything.
She told New: "A long time ago, in my early 20s, I had a fleeting relationship with a woman. It was just a one-off thing. I'd just come out of a bad relationship with a man and someone was there."
The 51-year-old explained that her former lover has claimed she is a lesbian but Byrne has insisted that this is not the case.
She commented: "She came out of the woodwork to say, 'I know Mary Bryne - she's a lesbian'. That's totally not true."
Asked if she gets a lot more attention from men since becoming famous, the singer replied: "Yeah, I do! But I'm not interested. It would take a lot for me to change my way of living. I'm quite content on my own."
Byrne also admitted that she turned down an offer to have a gastric band fitted for free.