Photos published by TMZ appear to show the actress with a large baby bump.
According to the outlet, Julia was with husband Danny Moder at his parents' Los Angeles home when she stepped out with a noticeable bump concealed by a baggy sweater.
Julia and Danny share three children. The couple are parents to nine-year-old twins Hazel and Phinnaeus and six-year-old Henry.
Julia may soon have to address the rumours head on as her next film, August: Osage County, is scheduled for US release Christmas Day and several promotional appearances are ahead.
She will also appear in forthcoming TV movie The Normal Heart, scheduled for release next spring.
The actress recently opened up about juggling her career and motherhood, joking that her agent has been trying to keep her as busy as possible before she becomes a full-time mom.
"As my career is slowing down, he thought, I've got to figure this out before she brings it all to a screeching halt in favour of car pools," she told the US edition of Marie Claire last month, admitting she doesn't mind taking time off until the right project comes along.
"The things that are correct for me will come to me at the time that I am interested in them and have the capacity, the understanding, to do them," she explained.
"When I miss out on a part, I can be bummed I didn't get it, but then I see who got it, and I think, Oh, well."
