The 16-year-old, who was controversially eliminated two weekends ago, told Look that she was "so strongly focused" on the show that she didn't entertain the notion of a romance.
Asked if she could see herself in a relationship with Cuthbert now, Henderson replied: "At the moment, it's hard to say. He's still in the competition.
"As soon as we're both out of it, it's going to go boom... At the moment [we are just] very close and good friends, but after the competition, I'd love to see him. I do want to spend time with him. Only time will tell."
Henderson went on to dismiss rumours of a romance with Union J's youngest member George Shelley, describing him as a "best friend", before noting that the entire group were "bawling their eyes out" when she was eliminated.
As well as Union J, Henderson said that she had found friends for life in X Factor judges Tulisa Contostavlos and Nicole Scherzinger.
"I never wanted any other mentor than Tulisa," she said. "Since my live audition there was an immediate connection between us.
"We formed such a close bond and it was horrible to lose one another. She was really shocked the night I left but she said: 'Don't worry, this is just the beginning for you. You just wait Mrs'."
"She gave my dad her contact details to stay in touch. She's a lovely woman."
To read the interview with Ella in full, see the new issue of Look, out now.
Watch Digital Spy's interview with Ella Henderson below: