Be expecting a baby/child
Definition 1 of 1
Pro Tip 1/3Expectation Nuance
Implies both pregnancy and anticipation for the upcoming birth, often used for emotional emphasis. 
They are expecting their first child and have begun decorating the nursery.
Pro Tip 2/3Time Frame
Typically used when the baby is due soon or the pregnancy is publicly known. 
With the baby expected next month, they are expecting a baby very soon.
Pro Tip 3/3Phrasing Sensitivity
Be mindful; the phrase can be personal. Use it respectfully, especially in new acquaintances. 
I heard you're expecting a child, congratulations!