Kardashian, Jenner's step-daughter, was first linked to the presenting role last month and was recently rumoured to be on a shortlist of candidates for the job.
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Jenner has now told Digital Spy that he is aware of the speculation.
"I heard the same rumour," he said. "It's been going round the house for a while. I don't know [if it's true]."
He added: "I honestly think she would be a great host. She's got the personality, she's fun, people like her - yeah, I think she could be very good."
Kardashian has previously admitted that she "would love" the hosting job on The X Factor USA, saying that she "would be honoured" to land the role.
Other stars linked to the series include Stacy Keibler, Glee's Kevin McHale and Pussycat Doll Ashley Roberts.
> Read our full interview with 'Keeping Up with the Kardashians' star Bruce Jenner
