The British royal chose his top tunes for the radio show UK Music & Memories, with Eimear featuring alongside The Three Degrees, Barbara Streisand, Edith Piaf and Diana Ross.
"On my annual visits to Ireland, north and south, I always look forward to what I know will be a feast of musical talent," the prince said on the show.
"In 2018 I had the enormous pleasure of hearing the singer Eimear Quinn performing at the St Patrick's Day dinner I attended in London. The Voice is the song, written by Brendan Graham and very Celtic in its feel, with which Eimear won the Eurovision Song Contest in 1996
"She recently re-released it in a recording with the RTÉ Concert Orchestra."
In an interview from her home in Geneva, where she lives with her husband Noel Curran, the director general of the European Broadcasting Union, and daughters, Joelene (11) and Marlene (9), Eimear tells the
Sunday World: "I was totally astonished. My God! How lovely, and especially when he was remembering the performance for the St Patrick's Day celebrations at the embassy in London.
"It was kind of personal in that way. It came out of the blue. I had no expectation whatsoever. It was just a lovely thing for him to say, and I was among such incredible company on his list."
It was Brendan Graham who asked Eimear to sing The Voice after he'd seen her perform with the group Anúna. It was the last of Ireland's seven Eurovision winners.
Eimear said: "It's a song that continues to be completely relevant to me in my work all the time. I perform it every single time when I do a concert, and will do when work resumes. It's still requested, it's demanded. It has been a gift to me. It's been a blessing.
"Singing in Eurovision has always been a blessing in my life. Eurovision remains an extraordinary event to this day. It's something that has been a huge positive in my life. It has given me the best start possible as a solo artist and allowed me to really develop as an artist and composer on a very high platform.
"The version of The Voice that Prince Charles refers to was one that I only released last year on an orchestral album called Ériu that I did with the RTÉ Concert Orchestra. Even though it featured a lot of very new material I still included it."
This year was the 25th anniversary of Dublin-born Quinn's Eurovision win, and to mark the occasion she recorded a video for YouTube on Eurovision night.
"I did a completely unaccompanied version of it, an a capella version, which is just basically Brendan's poem and melody and my voice. So we have decided to release it on all streaming platforms now, as a result of all the attention that Prince Charles has brought to it, the lovely exposure and lovely honour," Eimear reveals.
Earlier this year Quinn was voted in to the Classic FM Hall of Fame 2021 with her piece, In Paradisium. It's the world's biggest poll of classical music tastes, and Eimear's was chosen from 300 in a vote by listeners.
Brendan Graham, who wrote the global hit, You Raise Me Up, says it was "surreal" to be recognised by Prince Charles for penning The Voice. "It was a total surprise, but a welcome one," he tells me.
The Tipperary-born composer and author has written previous songs for members of the royal family, including This Mother's Heart, which was sung by Katherine Jenkins to celebrate the Queen's 90th birthday.