The singer and tech billionaire aren't officially together, however they currently co-parent X Æ A-Xii, Exa Dark Sideræl and Techno Mechanicus.
Page Six has obtained court records that show Grimes, real name Claire Boucher, has filed a 'petition to establish parental relationship'.
The outlet states this is sometimes done when the parents of children aren't married and it helps sets legal precedent over who the parents are.
The specific details of the case have been currently remained sealed.
It comes after Grimes lashed out in a series of since-deleted Twitter/X posts, according to the Daily Mail.
The 35-year-old demanded to be able to see her son and called out Shivon Zilis, who recently had twins with Elon Musk through IVF.
"Tell Shivon to unblock me and tell Elon to let me see my son or plz respond to my lawyer," she said.
"I have never even been allowed to see a photo of these children until this moment, despite the situation utterly ripping my family apart."
It was only revealed that Grimes and Musk had a third child when a review of a biography on the tech billionaire was done by The New York Times.
Musk and Grimes were first romantically linked to one another back in May 2018.
Two years later, they welcomed their firstborn X Æ A-12 into the world, and their second child came along in December 2021.
Their first daughter was conceived via a surrogate and she was named Exa Dark Sideræl Musk or 'Y' as a nickname.
They separated after Y and Grimes explained that she classed her relationship with Musk as 'fluid', her 'best friend' and 'the love of my life'.
Walter Isaacson's biography had a write up in The NYT and journalist Jennifer Szalai said: "The musician Grimes, the mother of three of Musk’s children (the existence of the third, Techno Mechanicus, nicknamed Tau, has been kept private until now), calls [Musk's] roiling anger 'demon mode' - a mind-set that 'causes a lot of chaos'.
"She also insists that it allows him to get stuff done."
That was how the world was introduced to the pair's third child.
According to the biography, Tau is the tenth child of Musk's - children he shares with three separate women.
Isaacson was able to gain such an insight into Musk's life by shadowing him for two years with 'unprecedented access' to his life.
Featured Image Credit: Frazer Harrison/FilmMagic. Instagram/Grimes
Topics: Elon Musk