The 16-year-old finalist is said to be "inseparable" from her rival hopeful, after they had been flirting for weeks, The Sun reports.
The pair were allegedly dared to kiss by the other contestants at a London hotel last week, and have now been seen regularly holding hands and texting each other.
"It's such a cute romance - they're playing it down but they're absolutely inseparable," a source said.
"They are holding hands when they think no one is looking and since they were dared to kiss, they haven't been apart."
Photo gallery - 'The X Factor' series nine - Week one performances:
Copyright: Ken McKay/Thames/Rex FeaturesBoth Henderson and Union J were voted into the second round of the competition in last night's show.
Henderson was voted as the first round's top singer by Digital Spy readers, while Union J were voted the worst.
New! Digital Spy breakfast show - watch Anna Williamson discuss the day's biggest stories including The X Factor, Homeland and Leona Lewis: