Further information is scarce, and representatives for the couple have yet to comment on the baby news.
Emma, whose father is actor Eric Roberts, was previously engaged to her "American Horror Story" co-star Evan Peters, but they called off their romance for good in early 2019, having dated on and off since 2012.
The "Scream Queens" actress is known for keeping her private life under wraps, and last year 2019, she explained why she was so closely-guarded.
"I never want to talk about relationships I'm in or that are ending or have ended," she told Cosmopolitan magazine.
"It's hard enough to be with someone by yourself, let alone with an audience. Growing up is hard. Sometimes it makes me sad that I can't have a private moment. Because of Twitter and Instagram, there's a whole other element where everybody can comment on what you're doing and no one knows the real story. That's hard."
Meanwhile, Garrett's exes include actress Kirsten Dunst. They ended a four-year romance in 2016.