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The rapper - who recently changed his name to Ye - married Kardashian in 2014, and the pair have four children together: North, Chicago, Psalm and Saint.
Kardashian filed for divorce in February, but West has now claimed that they are 'not even divorced' and he wants to be with her.
Referencing his ex's self-deprecating monologue on Saturday Night Live last month, the 44-year-old said on the Drink Champs podcast: "SNL making my wife say 'I divorced him' on TV because they just wanted to get that bar off, and I ain't never even seen the papers. We're not even divorced.
"That ain't no joke to me. My kids want their parents to stay together. I want us to be together."
You can watch the full interview here:
In the SNL monologue referenced by Ye, reality TV star and billionaire businesswoman Kardashian joked about their break-up, as well as her sex tape and OJ Simpson.
In a gag about West and former step-parent Caitlyn Jenner - both of whom have had failed bids for political office over the last 12 months - Kardashian said: "I'm not running for president - we can't have three failed politicians in this family."
And joking about her divorce, Kardashian said the reason she split from West was 'his personality'.
She said: "I married the best rapper of all time. Not only that, he's the richest black man in America.
"A talented legit genius who gave me four incredible kids. So, when I divorced him, you have to know it just came down to one thing: his personality."
Kim Kardashian West's Monologue! pic.twitter.com/t60b6ZC6cl
- Saturday Night Live - SNL (@nbcsnl) October 10, 2021
The 41-year-old elaborated on the background to the break-up in a more serious fashion in the finale of Keeping Up with the Kardashians, which aired in June.
In scenes filmed after Kim turned 40 in October last year, she said she had been speaking to a therapist and realised she was unhappily married.
"I just want total happiness," she told her mother.
"Obviously, I know complete bliss is not a full reality but if I can have it more the majority of the time, that's all I want to do.
"Wherever that takes me I just want my pure happiness. So that's what I'm working on, figuring out how to get there.
"I just feel I've worked so hard in life to achieve everything that I wanted to and I lived up to my expectations and achieved 10 times more than I even thought was humanly possible but I don't have a life to share that with."
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