The pair were recorded while in a dressing room at auditions in Liverpool, preparing to perform for judges Gary Barlow, Tulisa Contostavlos, Kelly Rowland and Louis Walsh, The Sun reports.
The unidentified hopefuls were caught out by cameras, which have been set up to capture behind-the-scenes footage.
"This was jaw-dropping stuff," a set source told the paper. "No-one knew what to do."
Police were not called to deal with the pair, but producers Mark Sidaway and Cat Lawson did order them off set.
Contestants who get through the initial auditions are being filmed at all times. However, it has been claimed that the singers - who do sign disclaimers - were unaware of the cameras behind the dressing room mirrors.
"This is pretty devious but the singers are mostly here for their five minutes of fame," the source added.
An X Factor spokesperson commented: "This was an isolated incident. The contestants involved were asked to leave immediately and did not perform before the judges. Contestants are made aware when cameras are filming them."
The two-way mirrors have also apparently seen "hundreds of contestants" caught stealing items from the backstage area.
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