Caitlyn Jenner and Kim Kardashian West. Picture: Instagram

Kim Kardashian West "cried hysterically" after seeing her former step-father Caitlyn Jenner - formerly known as Bruce Jenner - dressing in women's clothing for the first time.

Jenner came out as transgender in 2015, but her 38-year-old step-daughter Kim has claimed she had walked in on the former Olympian dressed as a woman long before then, and was left "shaking" and confused by what she had seen.

Kim - who was living in her mother Kris Jenner's home with Caitlyn at the time - said: "I found out when I was maybe 25. My mom was out of town and I walked in on Caitlyn all dressed up ... as a woman in the garage at my mom's house. I ran inside, packed a bag so fast, shaking, and ran out and called Kourtney. I said, 'I have to come spend the weekend with you.'

"I was hysterically crying. She just was like, 'What is it? Did you catch [Caitlyn] cheating?' And I was like, 'I wish. I don't know what I just saw.' I didn't come home for the weekend."

The 'Keeping Up with the Kardashians' star - who has North, five, Saint, two, and Chicago, nine months, with her husband Kanye West - says Caitlyn begged her not to tell her mother, and Kim "kept her mouth shut" for the sake of her younger sisters, Kendall and Kylie Jenner.

She added: "[Caitlyn said to me] 'One day I'll sit down and I'll explain this all to you, but until then, please don't tell a soul and please don't tell your mother. She'll kill me.'

"I thought, 'Okay, if I tell her I'm going to break up their marriage and my little sisters aren't going to have their dad around, so I better keep my mouth shut. I didn't say a word."

Since transitioning, Caitlyn has become estranged from much of her family following a scathing account of her relationship with Kris in her memoir, in which she claimed the 62-year-old matriarch never supported her.

But Kim says Kris was "so in love" with Caitlyn, and claims the family - who hosted a special of their reality show in 2015 dedicated to Caitlyn where she explained her transition - just want her to "be happy and be herself".

Speaking during an appearance on Alec Baldwin's ABC talk show 'The Alec Baldwin Show', Kim said: "She was so in love. She didn't think anything would be an issue in their relationship. Did she ever dream that [Caitlyn] would transition into a woman? I don't think that was ever something she would have dreamed in a billion years.

"That's why I love that we did share our story on our show, because it gave people the understanding that you can have every different emotion and that's okay. At the end of the day, we just want Caitlyn to be happy and be herself."