Reality television star Kim Kardashian is expecting a third child with rapper Kanye West via a surrogate, US media reported on Wednesday.

"The entire family is over the moon. Kim had been looking for a surrogate for months until recently when she found the perfect candidate," an unnamed source was quoted as telling People magazine.

"Given her health scares in the past, Kim felt the need to hire a surrogacy agency that helped serve as the liaison in finding a healthy woman who would be a great surrogate option for her and Kanye."

Kardashian, 36, and West, 40, were married in 2014 and have a son, Saint, who is 21 months old and a four-year-old daughter, North.

Celebrity gossip portal TMZ said their third child was due at the end of January.

US media have been speculating for several months that the celebrity couple may have hired a surrogate.

Kardashian has never confirmed this although she has wondered aloud about investigating the possibility on her E! cable reality show "Keeping Up with the Kardashians."

She has blogged about having placenta accreta, a condition that can cause complications during pregnancy in which all or part of the placenta attaches to the womb.

"My doctor had to stick his entire arm in me and detach the placenta with his hand, scraping it away from my uterus with his fingernails. How disgusting and painful," Kardashian said on her blog, recalling North's birth.

"My mom was crying; she had never seen anything like this before. My delivery was fairly easy, but then going through that -- it was the most painful experience of my life!"

Kardashian's representatives refused to comment.