Gary Barlow, Tulisa Contostavlos, Louis Walsh and Nicole Scherzinger have been told to pick one further act to join their final three, reports The Sun.
The public will then get the chance to vote for their favourite out of the four wildcards, with the most popular act sent through as the 13th finalist. This will leave one judge with an extra act.
The four wildcards are said to have already been picked and will be revealed on Sunday's show (September 30).
Photo gallery - The X Factor Final 24:
"With the standard so high this year, the judges had a tough time choosing their three, so this gives another amazing act the chance to perform on the X Factor stage."
The phone lines will remain open until the following Saturday, when the most popular act will perform with the other 12 finalists.
[Amelia Lily, who was given a second chance halfway through the X Factor live shows last year]
A similar wildcard element was used in the 2010 series, but each judge was given an extra act rather than just one.
Last year, Amelia Lily was given an extra chance halfway through the live shows, following the departure of Frankie Cocozza and a subsequent wildcard vote with other axed hopefuls.
Contostavlos has already lent her support to a Facebook campaign to bring back axed contestant Joseph Whelan.
The X Factor continues on Saturday (September 29) at 7.30pm on ITV1, where the acts will join their mentors for the Judges' Houses stage of the competition.
Watch X Factor hopeful Jake Quickenden talking to Digital Spy below: