While West and Kardashian have a four-month-old daughter together named North "Nori" West, the fact they're new parents reportedly hasn't impacted West's mindset on proposing.
"He doesn't feel like he has to marry Kim just because they have a daughter together," added the source.
Kardashian, who has wed twice and both marriages ended in divorce after short periods of time, is reportedly just fine with leaving her relationship with West the way it is.
"Kim feels like she's been there, done that when it comes to 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 told RadarOnline.
"It took her a while to learn the value of privacy, and to abandon the idea of another over-the-top wedding, but she's getting there thanks to Kanye's influence. Plus, she can't help but remember the humiliation she suffered after her 'fairy tale wedding' to Humphries ended in divorce."
However, the Kardashian clan allegedly still hopes the new mom and rapper will eventually tie the knot.
"The Kardashians don't exactly have a good track record with healthy marriages these days, so they're leaving Kim and Kanye alone to do whatever they want, as long as they're happy."
In August, sources told Us Weekly that Kardashian and West were planning a "secret" possible "destination wedding," as West wanted their big day to be "over the top" since it would be his first marriage.
"They've been discussing marriage for a while," a source told Us at the time. "A wedding is in the works."
Added a West friend, "He wants to get married more than she does!"
"I found what I really wanted. So I think I definitely do want that," Kardashian said of exchanging vows with West shortly after she had finally reached a divorce settlement with Humphries following months of court proceedings and legal battles over their 72-day marriage.
A source also told Us in January that West was "dying to propose" to his then-pregnant girlfriend. However, the fact Kardashian was still legally married to Humphries at the time prevented the rapper from popping the question.
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