The source said that during her relationship with her ex "Tyga, whenever things were good, Kylie said she wanted a baby. Between spending lots of time with her nieces and nephews, and being around Tyga's son, she claimed she was ready."
Meanwhile, "Her family would beg her to protect herself. They were very concerned."
Tyga, 27, has a four-year-old son called King Cairo by none other than Blac Chyna, who's since also had a daughter by Kylie's half-brother Rob Kardashian.
Travis, 25, has been dating Kylie since this April - the same month she and Tyga had publicly announced that they'd broken up.
The pregnancy story was broken on Friday by TMZ, which reported that Kylie's boyfriend Travis Scott is the father.
People claimed that day that Kylie's baby - allegedly a girl - is due in February.
A source had gossiped then that Kylie and Travis "started telling friends a few weeks ago. The family has known for quite some time. She is really excited and so is Travis."
Kylie, who owns two lavish homes in Hidden Hills, has yet to publicly confirm the pregnancy herself, as has Travis.
Nor have Kylie's parents Kris and Caitlyn Jenner - as well as Kylie's sister Kendall Jenner and four Kardashian half-siblings - confirmed the rumor outright.