Calling reports of his firing "a fabrication," a rep for Jones tells PEOPLE, "There have been absolutely no conversations about Steve Jones leaving The X Factor."
According to a show rep, "No discussions have been had and no decisions will be made about any contracts until the New Year."
In the meantime, "Steve is very happy with the outcome of this season," his rep says. "And he looks forward to being back and discovering more talent in the New Year."
The show's finalists – Melanie Amaro, Chris Rene and Josh Krajcik – return to The X Factor stage Wednesday (8 p.m. ET) on Fox to compete for the $5 million prize.