It was confirmed last week that the music mogul will not appear as a weekly judge on the next UK series of the show. Cowell will continue to play a role on the programme, but will focus on the judging panel for the US version.
Barlow was previously linked to the show, with reports at the time claiming that he was just "days away" from signing up.
According to the Daily Mail, a show insider has now confirmed that the Take That star is "our favourite for the job".
"We are in discussions and we should have something to announce in the next couple of weeks," the insider told the paper. "What Gary and Simon both have is an innate understanding of the music industry and what you need to succeed - that determination. Gary would be a great judge."
It is claimed that ITV bosses are now rescheduling auditions for May, to work alongside Take That's upcoming 'Progress Live' tour.
Dannii Minogue and Louis Walsh are both expected to sign new contracts for the show, while reports say that Cheryl Cole will officially quit if she is confirmed for the US judging panel.
An X Factor spokesperson said: "We will announce the new X Factor judges in due course and everything is speculation at this stage."
Meanwhile, a spokesperson for Barlow told Digital Spy that the latest claims are nothing more than "more speculative stories".
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