The new baby would join 23-month-old Penelope Scotland and four-year-old Mason Dash.
"[Kourtney] wants to have a handful of kids," added the insider.
The baby is reportedly due in December.
"They don't know the gender yet," another source explained. "They just want the baby to be healthy."
Kardashian reportedly stayed at the Trump SoHo hotel in New York City in late May following her sister Kim's European nuptials.
"Kourtney looked really pretty. She had a nice flush on her cheeks," a guest at the hotel told Us of Kardashian's "pregnancy glow."
Kardashian was also recently spotted on a double date with Disick, her sister Khloe, and Khloe's boyfriend French Montana in New York City and had abstained from drinking wine. She reportedly drank ginger ale instead.
Kardashian, 35, and Disick, 31, began dating in early 2007. Mason was born on December 14, 2009, and Penelope was born on July 8, 2012.