Multiple sources confirmed the news to the magazine, and several other publications have since confirmed the news. The couple, who welcomed daughter Chicago last January via surrogate, reportedly had one embryo left, a male, who is due to arrive "in very early May."
The couple are also parents to 5-year-old daughter North and 3-year-old son Saint.
One source said that Kardshian, 38, "always wanted four kids."
In August, after rumors surfaced of a fourth baby, Kardashian told E! News that "as of now" she and West were not planning for another child. "I've been really open about it and talked about it on our show, so I don't know," the KKW Beauty founder said. "We start filming season 16 [of Keeping Up With the Kardashians] next week, so if I think about it more and it's gonna happen, you'll definitely see it on the show. But as of now, no."
Previously, a source close to the couple said that she and West, 41, weren't "in a huge rush" to have another child after welcoming Chicago.
"They have absolutely talked about trying for another baby with the help of a surrogate, but nothing seems decided for sure," the source told PEOPLE. "Chicago is still little, and they have time."
"They don't seem in a huge rush," the source continued, adding that the couple would love for the same woman who carried Chicago to carry their next baby. "They would use the same surrogate if she agrees to help them again. Kim can't say enough kind words about the surrogate."
Another source told PEOPLE that "Kim and Kanye were already talking about baby No. 4 when Chicago was just a couple of days old. And they absolutely would use the surrogate again. They love her."
In an interview with ELLE last year, Kardashian opened up about using a gestational carrier to welcome Chicago into the world.
"I hated being pregnant," she said, referring to the complications she suffered during her first two pregnancies. "But as much as I hated it, I still wished I could have done it on my own. The control is hard at the beginning. Once you let that go, it's the best experience. I would recommend surrogacy for anybody."0comments
In that same interview, she said that four children would be her limit.
"I don't think I could handle more than that," she said. "My time is spread really thin. And I think it's important that in all couples, th mom gives the husband as much attention as the kids."