The 'I Dreamed A Dream'singer sees the Barbados-born beauty as one of her pop rivals, and believes the pair could work together on an R&B project, although she is unsure how it would sound.
She said: "I've got hard competition. But there are certain types of music that you're good at and certain types that you're not. I mean, would I be good at R&B? I suppose you never know.
"Maybe me and Rihanna could get together, I could dye my hair purple."
Although the 49-year-old Scottish star has performed in front of the Pope and seen her second LP 'The Gift'top album charts across the globe, she still dreams of meeting Beatles singer Sir Paul McCartney.
In an interview with The Sun newspaper, she said: "The Beatles are still around now, their records live on. I hope to be in the same calibre one day.
"I know I've got a lot to do yet though. I'd like to meet Paul. If he ever wanted to perform together, I'd have no problem with it - here I am, baby!
"But spiritually, meeting Paul would be up there as well."