Grimes has been experiencing "ups and downs" in her romance with Elon Musk.
The 32-year-old singer recently gave birth to the couple's first child, a son named X Æ A-12, but sources have said their romance could be on the rocks as they were reportedly "on and off" throughout Grimes' pregnancy.
A source told Us Weekly magazine: "Elon and Grimes have experienced a lot of ups and downs in their relationship throughout Grimes' pregnancy and have been on and off. Through it all though, they have and will continue to maintain a close friendship.
"Regardless of what happens to them romantically, Elon plans to be a father figure and be involved in the life of his child."
Meanwhile, the couple have both explained the meaning and pronunciation of their tot's unusual moniker.
Tesla and Space X founder Musk, 48, said: "It's just the letter X and then the Æ is pronounced 'Ash. A-12 is my contribution ... Coolest plane ever. It's pretty great."
He explained that Grimes "mostly came up with the name," adding: "Yeah, she's great at names."
While Grimes recently clarified the meaning behind her son's name, as she wrote on social media: "X, the unknown variable ... Æ, my elven spelling of Ai (love &/or Artificial intelligence) ... A-12 = precursor to SR-17 (our favourite aircraft). No weapons, no defences, just speed. Great in battle, but non-violent + (A=Archangel, my favourite song) (metal rat) (sic)"
However, the 'Delete Forever' singer accidentally got the name of the aircraft wrong, and Musk couldn't stop himself from jumping in to correct her.
He wrote: "SR-71, but yes," in reference to the aircraft and it didn't take Grimes long to put him in his place.
She tweeted: "I am recovering from surgery and barely alive so may my typos b forgiven but, damnit. That was meant to be profound (sic)."
Musk quickly backed down and wrote: "You are a powerful [fairy emoji, queen emoji]."
X Æ A-12 is Grimes' first child, while Musk has five children with his former wife Justine Wilson. The former couple also had son Nevada together but he died of sudden infant death syndrome at 10 weeks in 2002. — BANG