E! News reports that the Glee star was offered the chance to front the Fox singing competition following former host Steve Jones's axing from the series.
Criss is said to have refused the job due to his numerous career commitments with Glee and other projects.
"They were after him. But there's no way he could have done it with everything he has going on," a source told the website.
Steve Jones has insisted that he has no hard feelings over his firing from The X Factor USA.
Show boss Simon Cowell has remained coy over rumours that Britney Spears is in line to join the show's judging panel as a replacement for one of the departing first season mentors Nicole Scherzinger and Paula Abdul.