Britney, 23, and her husband Kevin Federline announced the pregnancy in April.
Reports suggest that they will call the baby either London Preston or Preston Michael. Her top name for a girl was Addison Shye.
It is the first child for Britney, while Kevin, 27, has two young children -- Kori, three, and one-year-old Kaleb -- with ex-girlfriend, Shar Jackson.
Last month, the singer revealed: "I have a feeling I'm going to have an operation. I don't know why but I hope so.
"My mom said giving birth was the most excruciating thing she's ever gone through in her life. So if a caesarian doesn't happen, I'll be like, 'Epidural, please.' "
The star, who has sold more than 60 million albums, has made no secret of her wish to start a family and has said she can see herself as a mother.
Shortly after tying the knot in a private ceremony last September, she announced she would be taking a break from music to enjoy married life and focus on motherhood.
"I've had a career since I was 16, have traveled around the world and back and even kissed Madonna," she wrote on her Web site.
"The only thing I haven't done so far is experience the closest thing to God and that's having a baby. I can't wait."
Britney hosted a Moroccan-themed baby shower at her Malibu home last month.
Presents included a white wrought-iron bassinet from her mother, Lynne, a car seat, a stroller, an infant bathtub and lots of stuffed animals.
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