The actress is a huge fan of the Scottish singer and said watching her sing I Dreamed A Dream - which Anne now sings in the upcoming Les Miserables movie - never fails to cheer her up.
She said: "Before I knew that I was going to play Fantine, I used to watch that clip when I was having a low day. It made me feel so wonderful.
"The other thing that's also fun is to watch Simon Cowell's mind racing as both a producer and an adding machine. I just love that clip."
Anne said it was "really exciting" getting to perform the song in Tom Hooper's musical drama.
"I'd never sung on film live before and that was a really new thing to wrap my head around because I'm a musical theatre geek and so I've been taking classes since I was very young and I'm used to song interpretation and telling a story through song that resonated with however big the audience is that you're playing to," she said.
"But the language of film is totally different so it was really exciting to take this iconic song that is so beloved and find a way to put it through the prism of film.
"That meant going very deep inside myself to some uncomfortable places but that's what we do and those are the jobs you remember and the ones that make you grow."
Les Miserables opens in the UK in January.