The 35-year-old teamed up with the professional dancers for a performance on The Greatest Dancer last weekend.
Katya, 29, posed for pictures with Cheryl after the performance, and now The Daily Star reports the singer asked her for secret dance lessons.
Katya said: "Cheryl wanted to know everything.
"She was saying to me: 'Katya show me how to move my hips, show me your arm movements, what do I do?'
"And then she was practising. She was loving it. And she was really good."
Strictly head judge Shirley Ballas previously revealed she would love to have Cheryl on the show as a contestant.
And Katya agreed, saying: "We do like a pop star on Strictly. So you never know, she could be on the next series."
Shirley, 58, previously told The Sun: "There’s a few names bouncing around but I’m open to anybody that goes on.
“I would like to see Cheryl Cole on it. You know, I think she would make a great contestant.”
Strictly bosses are already on the hunt for celebrities to take part in the 2019 series.
So far, Chris Evans, Alan Carr and Huw Edwards have all been linked to the show and could be seen in their sequin shirts come September.
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