Jones's future on the series was thrown into doubt this week when an X Factor insider told The Mirror that the Welsh presenter will likely be sacked following Thursday (December 22)'s first season finale.
The source claimed: "The executives at Fox have already decided not to renew his contract and so, short of a miracle happening, it is pretty much a done deal that he will not take part next season."
A spokesperson for Jones has denied the validity of those claims, insisting to ET Online that the host has no plans to leave The X Factor.
Jones's rep commented to the website: "The Mirror story is a fabrication that we would have corrected had we been called for comment. There have been absolutely no conversations about Steve Jones leaving The X Factor.
"Steve is very happy with the outcome of this season and he looks forward to being back and discovering more talent in the New Year."
Jones himself joked about the firing rumours during an interview on British television programme Daybreak on Tuesday (December 20).
"I'm happy with the way I performed over the course of the series, and hopefully Simon Cowell is as well," Jones said. "It's difficult to gauge Simon because he only ever approaches you and talks to you when you've done anything wrong."
Cowell has admitted that he was too "cocky" while promoting the first season of The X Factor earlier this year and acknowledged that it's going to take "a little bit longer" for the US version of the series to match its UK success.
Melanie Amaro, Josh Krajcik and Chris Rene compete for The X Factor's $5m grand prize on the two-night finale, airing tonight and Thursday, December 22 at 8/7c on Fox.
> Simon Cowell: 'X Factor USA final will have the greatest talent'
> X Factor USA: Nicole Scherzinger won't commit future to show
Watch Nicole Scherzinger perform 'Pretty' on last week's X Factor results show below: