Multiple sources told Page Six the couple are "done" and Kim has hired A-list divorce lawyer Laura Wasser. It is said Kim, 40, and Kanye, 43, are trying to keep the proceedings "low key" and they are in "settlement talks."
A source told People the rapper understands their marriage is over and he is bracing for a divorce filing but doesn't know when it will happen.
Representatives for the stars have yet to comment on the matter.
The reports of divorce come after ones that previously said Kim and Kanye have been leading separate lives.
Kanye attended Kim's extravagant 40th birthday party in October in Tahiti. But it is believed the pair have been spending time apart, with Kanye staying mostly on the family's Wyoming ranch, while Kim has set up base in Calabasas, Calif. with the couple's children: daughters North, 7, and Chicago, 2, and sons Saint, 5, and Psalm, 1.
At the end of November, the beauty mogul uploaded a photo of her and Kanye to celebrate the 10-year anniversary of his My Beautiful Dark Twisted Fantasy album.
The couple endured some very public difficulties over the last year, including Kanye sharing personal details about the family and his relationship with Kim on Twitter. In July, the reality star shared a lengthy post about her husband's bipolar disorder diagnosis.
"Anyone who has this or has a loved one in their life who does, knows how incredibly complicated and painful it is to understand," she wrote.
"I've never spoken publicly about how this has affected us at home because I am very protective of our children and Kanye's right to privacy when it comes to his health. But today, I feel like I should comment on it because of the stigma and misconceptions about mental health.
"Those that understand mental illness or even compulsive behavior know that the family is powerless unless the member is a minor," she continued.
She encouraged fans to give her husband some "grace" during the difficult period.
"I kindly ask that the media and public give us the compassion and empathy that is needed so that we can get through this," she finished. "Thank you for those who have expressed concern for Kanye's well-being and for your understanding."
Kim and Kanye wed in May 2014 in a lavish ceremony in Italy, but they have a long history. They are believed to have first met in 2003, when Kim was married to her first husband, Damon Thomas. Kim and Kanye remained friends over the years.
After Kim's 72-day marriage to second husband Kris Humpries in 2011, "Kimye" officially became a couple and had several red carpet appearances in the following year. At the end of 2012, the pair confirmed they were expecting their first child, who they eventually named North. Since then, Kim and Kanye have remained one of the most high profile couples in Hollywood and entertainment circles.
We wish the family well during this time.