Kim Kardashian gave birth to a baby girl Saturday with boyfriend Kanye West by her side, and a new report has indicated that their daughter's name will begin with the letter, "K."

While the couple has yet to reveal the baby's name, a source told E! News that Kardashian previously told friends and family that the baby's name will start with a "K" after new parents' name.

The reality star reportedly also told friends that she and West discussed using his mom's name, Donda, who passed away in 2007, as the baby's middle name.

Back in March, it was rumored that West wanted to name the child "North West."

The 32-year-old is said to have given birth five weeks earlier than her reported due date on July 11. The reality star delivered the baby girl at Cedars-Sinai Medical Center five weeks early. 

A source from the hospital told Us Weekly that Kardashian felt ill Friday. 

"She's five weeks early. Kim got sick last night and had the baby early," the source said.

Despite the early delivery, Kardashian and baby is said to be doing just fine.

"Kanye was there with Kim when she went to the hospital and had the baby," a source said.. "She started to feel sick late [Friday] and was having contractions."

"They're all doing great and amazing," the source added.

Fans of Kardashian first learned that she was having a girl after she revealed the baby's sex on the premiere of her-hit family show, Keeping Up With The Kardashians. 

"I'm so excited we're having a girl," Kim said on the episode. "Who doesn't want a girl? I think they are the best. I know that's really what Kanye has always wanted - he wanted a little girl." 

West first announced to the world Kardashian's pregnancy at in concert in Atlantic City, NJ in Dec. 

He broke the news singing "Now You Having My Baby" while telling the audience crowd to congratulate his "baby mom," saying it was the "most amazing thing."

Kardashian later confirmed the news on her website, "It's true!! Kanye and I are expecting a baby. We feel so blessed and lucky and wish that in addition to both of our families, his mom and my dad could be here to celebrate this special time with us."

Tags: Kim Kardashian Kanye West