The "Keeping Up with the Kardashians" star will welcome her second tot with her on/off partner Travis Scott, who is also the father of Stormi.
The source added to People magazine: "She has been wanting to give Stormi a sibling for a while. She loves being a mom.
"She is thrilled that she and Travis are pregnant again. She has been enjoying her pregnancy in private. She has only spent time with close friends and family."
Kylie and Travis have not yet confirmed pregnancy reports, but the Kylie Cosmetics founder previously said she had "no plan" to give Stormi a sibling just yet.
Speaking in March last year, she said: "My friends all pressure me about it … They love Stormi.
"I definitely feel pressure to give her a sibling, but there's no plan."
The beauty had also said she wants "seven kids" in the future, but doesn't want to expand her brood right away. She added: "I want seven kids down the line, but not right now. Pregnancy is just not a joke; it's a serious thing and it's hard.
"I'm not ready for that just yet."
Meanwhile, Kylie recently said she was "blessed" to have Travis in her life as the father to her daughter.
Posting on social media for Father's Day in June, she wrote: "happy father's day @travisscott [heart emoji] one day isn't enough to honor the dad you are. we are so blessed to have you .. [heart emoji] (sic)"