Kardashian was first linked to the job in July and was recently rumoured to be a frontrunner.
Cowell has now revealed that the reality star is being considered during an appearance on The Ellen DeGeneres Show.
"We have screentested a load of people," he said. "I know who I would like, but no, I've got to get it approved by the network, so I think it would be wrong to say at this point just in case the network say no."
Pushed by DeGeneres to name some possible candidates, Cowell replied: "It could be a Kardashian. It could be a Kardashian. I think that would work.
"I mean, I'm quite a fan of not putting hosts on this show because I think it's going to give it a different dynamic, so we've got to find people who've got a great chemistry. But Khloe's definitely up there in the running."
Kardashian's step-father Bruce Jenner has previously told Digital Spy that he thinks she would be "a great host".
The X Factor USA will premiere on Wednesday (September 12) on Fox.
Watch Simon Cowell and Britney Spears on The Ellen DeGeneres Show below: