The 16-year-old auditioned with a self-penned track dedicated to her late grandfather, but has only performed cover versions in the competition's subsequent stages.
Speaking to Digital Spy and other journalists, Henderson said: "I'd absolutely love to do one of my own songs on the show.
"Each week we get given a theme, so it's about feeling a song [that] is 100% the one you want to use for that week, but no, nothing's stopping me from doing my own songs."
Henderson admitted that performing an original song at her first audition had been a "nerve-wracking" experience, saying: "I can remember feeling, 'Oh my god, this is such a huge risk I'm taking', but [it was] a once in a lifetime opportunity."
She also revealed that there are "stupid and funny and upbeat" original songs in her repertoire, as well as emotional ones.
Watch Ella Henderson perform an original song on X Factor below: