Rose Byrne Expecting Baby No. 1 with Boyfriend Bobby Cannavale

Rose Byrne is expecting!

The 36-year-old "Spy" actress was photographed on Thursday with a noticeable baby bump under her plaid shirtdress. The Aussie and her beau, "Boardwalk Empire" actor, Bobby Cannavale have not confirmed the news but several media outlets have.

The baby would be the first child for the couple, who started dating in 2012. Cannavale, 45, has a 20-year-old son with ex-wife, screenwriter Jenny Lumet.

Although Byrne and Cannavale are pretty private about their love life, Cannavale has publicly called Byrne the "love of my life," during his acceptance speech at the 2013 Emmys. Cannavale has also praised her work ethic.

"She's one of those people who are just really good at acting. Like me, she doesn't spend a lot of time talking about it," he told InStyle magazine back in May. "She does her work quietly, but she makes choices nobody else would make."

Byrne, who says she is not a romantic, has talked about how much she enjoyed working with Cannavale. They have starred in three movies together, "Spy," "Annie" and "Adult Beginners."

"Clearly, it could have not been a good idea, but it was very fun to have a really great friend on set," Byrne said to Elle Canada in 2014. "It was nice to share our day."

Byrne has also gushed about Cannavale's cooking skills.

"Bobby's a great cook. He's Cuban and he does a couple of really good Cuban dishes like arroz con pollo and Cuban cocktails," Byrne said to PEOPLE. "He's better than I am. I'm the good cleaner after!"

The couple recently forked over $2.2 million for a Boerum Hill townhouse in Brooklyn, NY.

Byrne's upcoming work include "The Meddler," "Neighbors 2: Sorority Rising," "X-Men: Apocalypse" and "The Something." Cannavale can be seen in the upcoming HBO TV series, "Vinyl," which airs in 2016.