The 43-year-old rapper took the Internet by storm when he unleashed a flurry of tweets making various claims about his home life, including implying that Kardashian's mother, Kris Jenner, will no longer be able to see the children he shares with the 39-year-old reality TV star.
West and Kardashian share four children: North, 7; Saint, 4; Chicago, 2, and Psalm, 1.
In since-deleted tweets, West said: "Kriss don't play with me you and that calmye are not allowed around my children. Y'all tried to lock me up," according to People magazine.
The message apparently rubbed Kardashian the wrong way, as a source told the outlet that she's "most upset" over the comment.
"She was most upset that [Kanye] said that Kris isn't allowed around the kids," said the insider. "Nothing could be further from the truth. Kris is an important part of the kids' lives and Kim loves the bond they have. She's 100% allowed around the kids."
Reps for Kardashian declined to comment when reached by Fox News.
Jenner, 64, often posts photos of her grandchildren, including Kardashian and West's own kids, on her Instagram.
Most recently, she wished North a happy birthday in June, sharing a series of pics. In one photo, Jenner sat with Kardashian and North in the grass.
"Happy Birthday to my beautiful granddaughter Northie!!!! From the very first moment we met on the day you were born, you have brought all of us so much happiness and joy!!" read the post's caption. "You are so creative and talented and funny and kind and you have the biggest best heart... what a blessing you are Northie. I love you to the moon and back and cherish every moment we get to be together."
Psalm also recently received a birthday wish, which was attached to a photo of Jenner planting a kiss on his head.
Rumors of strife between the pair were reported after West's campaign rally on Sunday, in which he claimed that he and Kardashian considered aborting their first child.
"Kim is shocked that Kanye spoke about North at the rally," a source told People. "She is furious that he shared something so private."
Another said claimed that "things have broken down significantly between the two of them, and it’s happened pretty suddenly."