Kourtney is already mother to two children with boyfriend Scott Disick, but has always wanted a larger family, according to the report.
A source close to the pair claims that Kourtney "always planned to add to her brood straight after her one-year-old daughter was born."
Kourtney and Scott, who welcomed son Mason in 2009 and daughter Penelope in 2012, have neither confirmed nor denied the reports, although Kourtney has raved in the past about her love of motherhood.
Following the birth of Mason, she told Parenting, "I think motherhood is just about instinct. I remember coming home from the hospital and having no idea what we were doing. Scott and I changed his diaper together, but after a day, it was like 'Oh!' I got it."
She echoed a similar sentiment during her second pregnancy, telling Parents magazine of her transition into motherhood, "It's definitely my favorite role in life. It has changed me and made me realize there is nothing else I would rather do with my time. Being a mom is what life is about. I hope people realize what the priorities in life should be and know not everything has to be perfect."