According to Us Weekly, the couple's surrogate, who they used to welcome now 11-month-old daughter Chicago into the world, is now pregnant with a boy - with the baby due "in very early May".
The news comes after it was reported that the couple, who are also parents to five-year-old North and three-year-old Saint, had one embryo left - a male.
Another source told the publication that Kim, 38, "always wanted four kids". The baby news was also tweeted by Us Weekly editor Jen Peros.
On an episode of the family reality series "Keeping Up With the Kardashians" last year, Kim told her pal Larsa Pippen that her rapper husband had been "harassing" her to have more children.
"Kanye wants to have more, though," she said. "He's been harassing me. He wants like seven. He's like stuck on seven."
However, Kim wasn't so sure about the number, admitting to Larsa: "(Seven kids is) crazy. I could never, especially in like the world we live in... I've been kinda hesitant about having more kids because it literally keeps me up at night, thinking about how my kids will survive in a crazy world like this."
While Kim carried North and Saint, she suffered complications in the pregnancies which meant she wasn't able to fall pregnant again herself.
She and Kanye turned to a gestational carrier to have a third child, the term which refers to a woman who carries a child she has no genetic connection to herself, and Kim expressed her gratitude in a post on her app after welcoming daughter Chicago.
"I'm so grateful for modern technology and that this is even possible," she wrote. "It's not for everyone, but I absolutely love my gestational carrier and this was the best experience I've ever had. Our gestational carrier gave us the greatest gift one could give."
"The connection with our baby came instantly and it's as if she was with us the whole time. Having a gestational carrier was so special for us and she made our dreams of expanding our family come true. We are so excited to finally welcome home our baby girl."