The reality star is on a shortlist of six candidates for the presenting role, according to TMZ.
However, Kardashian will reportedly have to do a screen test for the job before producers will consider hiring her.
It is thought that every person on the shortlist will have to audition for the post, with screen tests reportedly taking place during the next two weeks.
Kardashian, who was first linked to the X Factor hosting job last month, recently said that she "would love" the role and "would be honoured" to be picked.
Other stars who have been linked to the show include Stacy Keibler, Pussycat Dolls star Ashley Roberts and Terrence J.
Simon Cowell has previously claimed that The X Factor USA's new season will be hosted by a man and a woman.