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.
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: