The supermarket worker was linked this past week to Wagner but Byrne's focus is not on men.
Byrne, speaking to the Herald newspaper, said that music is her first love and "that's what I feel I'm married to now -- I've no time for anything else," she said.
On Wagner she said, "He's a lovely man but he definitely wouldn't be my cup of tea and I don't think I would be his. He likes the young women, you know! I'd go for someone around my own age or about 45, between them two."
On her sailing through to the following round, Byrne, 50, said it was "brilliant."
"The amount of support the people back home have been giving me is amazing. My family have been sending me updates the whole time and I'm just bowled over by the whole thing. It's just been unreal," she said.
Byrne also received a huge compliment from superstar Katy Perry.
Perry, who performed on the show last week, said she was a big fan of Byrne's and hoped she would do well.
Irish judge Louis Walsh reveled how much the "Kissed a Girl" singer liked the Dublin woman.
"Katy's mad about Mary's voice, she thinks there's something so soulful about it.
"She has definitely been one of Katy's favorites since she picked her at the Dublin auditions, she has a real soft spot for her," he said.
Walsh is confident Mary would go all the way to the finals.