But that lack of public action doesn't mean things are quiet behind the scenes.
New reports state that the reality star is plotting to seek full custody of the four young children she shares with her husband of six years.
All four children are currently in Kim's care at the multi-million dollar California mansion she painstakingly renovated with Kanye, where they spent Christmas without him.
A source told The Sun : "Neither of them want to seem like the loser in this divorce and they both will fight hard for their kids.
"Kim has made it clear she wants full custody so if Kanye tries to fight her on that, the custody battle will be brutal."
As news of the looming divorce made headlines, Kim's desire to put their children first was said to be at the heart of her planning. The couple share North, seven, Chicago, two, Saint, five, and one-year-old Psalm.
Sources told E! : "She wants to make sure she's making the right decision for the kids."
And they added: "It's not about the marriage anymore, she'll always care for Kanye but it's over between them.
"Kim is only focused on what's best for the kids. It's a tough decision for her and she's figuring it out."
Kim is also said to be keen to take possession of the property where they are currently staying, which is in the Hidden Hills neighbourhood where the 40-year-old's sisters and mother also live.
While Kanye is now said to be at their $14million Wyoming ranch, her plan is complicated by the vast cost of the huge California property.
Kanye masterminded the complete multi-million renovation of the mansion alongside Belgian designer Axel Vervoordt, with the results featuring in Architectural Digest.
All in, the couple spent around $40million for the house alone, before their estimated $20million renovations.
Kim owns the ground on which the house stands, plus surrounding lots. However, Kanye owns the actual house.
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