With the child taking her father Kanye’s surname the youngster would be “North West”.
According to InTouch magazine: “North is at the top of the list of names.”
A friend of Kim Kardashian and Kanye West told the magazine: “They’re not totally sure about it. Kanye loves it, Kim is okay with it.”
Prior to the baby’s birth on Saturday it had been expected that the pair would continue the “K” theme that runs in Kim Kardashian’s family.
Kim Kardashian, 32, has mentioned in the past that it will likely begin with a “K”.
And it seems her family is keen that remain the plan.
“The family doesn’t like it [North],” the insider told InTouch magazine.
The source added: “They’re going to decide by today [Tuesday].”
Kim Kardashian’s close friend Larsa Pippen revealed that she had been to visit the baby in the hospital and a decision was nearly made.
But she said Kim Kardashian didn’t welcome her suggestions.
“We kind of went back and forth and the name that I wanted, [Kim Kardashian] didn’t love,” Larsa Pippen said.
Kanye West has not spoken publicly following his daughter’s arrival.
But the rapper did take to Twitter on Tuesday morning – to promote his new album Yeezus as it was released.
“Yeezus album now available,” Kanye West tweeted.
Kanye West curtailed his promotional activities when Kim Kardashian told him she “felt strange” on Friday, instead flying to be at her side.
With the baby not due until July it had been planned that Kanye West would have time to finish his work commitments before the birth.
Despite his disagreements with Kim Kardashian over the name, Kanye west is said to be thrilled to be a first time father at 36.
Larsa Pippen revealed the pop star has hardly left the room since Kim Kardashian gave birth naturally at a hospital in Los Angeles on Saturday.
“He’s so cute. He doesn’t leave the room,” she told E! News.
“He’s, like, in love with the baby. It’s so cute.”
The wife of NBA superstar Scottie, Larsa Pippen, a reality star herself is a close friend of Kim Kardashian’s.
“She’s doing great,” the Real Housewives of Miami star said of Kim Kardashian.
“She’s feeling really good and excited and the baby is so freaking cute. She’s so cute.”
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