The Duchess of Cambridge is said to have paid homage to the singer by performing 'Fight For This Love' in a full body suit and split trousers, similar to those worn by Cole in her music video.
While backstage at the Queen's Diamond Jubilee concert, Prince William allegedly told Cole: "Did you know you've got a bit of competition?"
"She even learned the dance routine and was step perfect by all accounts," Cole revealed in her autobiography My Story.
"I could just imagine her and it was so surreal."
Cole also spoke about meeting Prince Harry backstage at The X Factor when he visited the show with girlfriend Chelsy Davy.
"I walked in and the scene was mental," she said.
"There were women partying everywhere and Simon was grinning like the Cheshire cat.
"Prince Harry was lying on the dressing room floor, with his top buttons undone, relaxing with a glass of wine in one hand and a cigarette in the other."
Cheryl Cole's My Story was released in stores yesterday (October 11).
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A year of the Duchess of Cambridge:
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