Melissa Armstrong auditioned for the show in Newcastle earlier this year, but her appearance was not screened on the show, which concluded its audition phase on Sunday (September 16).
The 21-year-old said that she expected to have her audition broadcast considering her family connection and link to the show.
"I have no idea what's going but it doesn't look like I am going to appear," she told The Sun.
Louis Walsh and Nicole Scherzinger reportedly put her through to the next round, but her performance of Cole's 'Promise This' did not impress Gary Barlow or Tulisa Contostavlos, and she did not progress any further.
Armstrong said that she is disappointed after producers gave her the impression she would feature on the show.
"Everybody is angry that Melissa's audition has been scrapped," one family friend said. "We can't believe it. She gave a really good performance and believed she would be featured in the audition shows.
"But after it was announced Cheryl was making her surprise comeback, it all went quiet. I wonder why that is?
"If anything, Melissa is a better singer than Cheryl. It's so unfair."
Cole will join Gary Barlow for the Judges' Houses stage of the competition.
Watch Cheryl Cole performing 'Promise This' on a live X Factor results show below: