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.
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