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Rex Features
The music mogul joined Louis Walsh, Dannii Minogue and Cheryl Cole in Glasgow for a new set of auditions on Monday.
Last year's run of the ITV1 talent show saw persistent rumours of a feud between Minogue and Girls Aloud star Cole, who joined the panel as a replacement for Sharon Osbourne.
A source told the Daily Star: "Simon says he wants the show to focus on the acts and not the judges."
However, crew members reportedly believe that Cowell is unlikely to see his wish granted over the coming months.
The insider explained: "Ultimately with such explosive personalities something will kick off."
The X Factor will return to screens in August.
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