Has the reported surrogate for reality star Kim Kardashian and her husband, rapper Kanye West, become pregnant?

People magazine, citing anonymous sources, said Wednesday that the surrogate is carrying the couple’s third child.

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The magazine said on June 21 that it had confirmed a report first appearing earlier that day at TMZ.com, saying Kardashian, 36, and West, 40, had already begun the surrogacy process.

TMZ said Wednesday that the baby was due in late January.

Kardashian had suffered from early-onset pre-eclampsia and delivered her first child, daughter North, 4, almost six weeks early. She additionally suffered from placenta accreta, a high-risk condition in which the placenta grows too deeply into the uterine wall, requiring surgery to remove. During her second pregnancy, Kardashian had to undergo an external cephalic version (ECV) to manually turn son Saint, 21 months, from a breech position to a head-down position.

Despite a history of fertility issues and troubled pregnancies, Kardashian has nonetheless said she wants to have a third child. “I’m going to try to have one more baby,” Kardashian told sisters Kourtney and Khloé Kardashian and their mother, Kris Jenner, in a March episode of E!’s “Keeping Up With the Kardashians.” She then said to the camera in an insert, “I want my kids to have siblings, but the doctors don’t feel like it’s safe for me.”