Kardashian ducked questions about West on Today last week following a series of public appearances with the rapper.
"I completely respect and understand that you have to ask these questions, but as I've said before, Kanye and I have been friends for years," Kardashian told Ann Curry. "You know, you never know what the future holds or where my life will take me."
Stern criticised Kardashian for now refusing to speak about her private life after previously filming her lavish wedding to estranged husband Kris Humphries.
"She thinks she's Jen Aniston now," the America's Got Talent judge joked to Extra.
Stern went on to predict that it won't be long before Kardashian tries to use the relationship to gain more publicity.
"The second her show gets a dip in the ratings... she'll have Kanye in his underwear, dancing on her show," he quipped.
A friend of West claimed this week that the 'Theraflu' star has fallen "genuinely head over heels" for Kardashian and wants her to be "[his] Beyoncé'.
> Bruce Jenner on Kim Kardashian, Kanye West: 'I'm not that excited'
> Howard Stern on judging America's Got Talent: 'I'm very confident'
Watch Howard Stern comment on Kim Kardashian below: