The hip-hop star has a daughter called Nori with the reality TV star and there has been speculation they are planning to wed in Paris.
Kim is always thought to have been unsure about tying the knot as she is twice divorced, with her union with Kris Humphries lasting just 72 days. Now it's claimed Kanye is also happy to keep things as they are.
"Kanye is telling friends that he’ll never marry Kim. He has no need or desire to make their relationship official in the eyes of the law," an insider told Radar.
"Kanye prefers the idea of them as partners. He sees marriage as outdated and he’s all about embracing the modern and the new. He doesn’t feel like he has to marry Kim just because they have a [daughter, Nori] together.”
This is said to fit well with Kim's outlook, which has changed over the last year. Her daughter is her main priority and she apparently has no interest in a "big splashy" wedding.
"She used to be so much more into the fame game, but now that she’s drifting away from the family and trying to do her own thing, she’s becoming more adamant about doing things on her own terms and keeping it low-key," the source explained.
The TV star is very close to her family, including mom Kris Jenner and sisters Kourtney and Khloé. Some of her loved ones apparently still want her to exchange vows with Kanye, but she is sticking to her guns and they are said to be "coming around".