The couple enjoyed a one-night stand, according to the Daily Star Sunday, and had hoped to keep their fling a secret.
But their identities are now said to have been revealed on Twitter.
“This is the last thing the two of them wanted,” a Strictly Come Dancing insider told the publication.
“Once something is on Twitter it is very difficult to control.”
The unnamed stars are apparently both known to millions.
They are said to have had an “instant connection”, the publication reports.
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After filming one Saturday evening, the couple apparently got together for a night of passion.
And when they arrived at rehearsals the next day “red-faced”, they did their best to keep it a secret.
However, after confiding in close friends, it didn’t take long for some of the Strictly staff – including the cameramen – to find out.
The source continued: “To have their identities leaked online is a complete nightmare. It started as a bit of flirting and suddenly they’re the latest in a long line of romances on the show.”
OK! Online has contacted a representative for Strictly to provide a comment.