The reality TV star is said to be the top choice with show bosses among the women who have auditioned for the role, reports TMZ.
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© Fox / Ray Mickshaw
Kardashian has been linked with the presenting role since July, while she herself has expressed a huge interest.
She has reportedly completed a successful screen test, with producers including Simon Cowell believing she would be the best choice in order to attract younger viewers.
A decision will be finalised in the coming days, while the host will not appear on the Fox series until the live shows begin next month.
A source said: "There's at least an 85% chance she'll get the job."
NBC's The Voice and The X Factor USA are set to go head-to-head during primetime next week.
Watch Simon Cowell being discussed by the other X Factor USA judges below:
