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Rose Byrne, Ring

PMC Images / MEGA

First comes baby, then comes marriage...?

Nine months after welcoming son Rocco Robin Cannavale, rumors are swirling that Rose Byrne and Bobby Cannavale. Byrne has been spotted wearing a diamond ring while out and about in Sydney, where she's currently starring in a production of David Mamet's Speed-the-Plow. The play, which opened Nov. 8 and co-stars Damon Herriman and Lachy Hulme, runs until Dec. 17.

E! News has reached out to reps for the stars, who began dating in 2012.

If there's anything they might love more than each other, it's performing for a live audience. "I'm such a big theater-goer, and obviously Bobby is, you know, Bobby Broadway," Byrne told Playboy as she was promoting X-Men: Apocalypse in June. "We're a couple of theater geeks."

Rose Byrne, Ring

PMC Images / MEGA

Both stars have been successful onstage, and Rose and Bobby have made quite a splash on the big screen, too. As it happens, they've appeared onscreen together three times—in Spy, Adult Beginners and Annie. According to Rose, it's "not particularly" difficult to work with her fiancé. "I imagine it would be more of a challenge if one of us were directing the other. As with any creative endeavor, you want the best for them. So if it's a failure, or if it's not going well, it can be heartbreaking. When we're working on something together, the stakes can feel pretty high."

Details regarding the reported proposal have not been revealed. This will be the first marriage for Rose and the second for Bobby, who has a 21-year-old son, Jack Cannavale, with his ex-wife.

Rose Byrne

Instagram

Last week, during an appearance on the Australian morning show Today, host Lisa Wilkinson accidentally referred to Bobby as Rose's spouse. "You told a great story about when you met your husband," Lisa said. "You quickly discovered that one of his best mates was Jon Hamm."

Rather than correct the co-host, Rose—who had just presented GQ Australia's International Man of the Decade award to Hamm—retold the story. "We weren't dating very long and he casually mentioned he was best friends with Jon," the actress told the hosting panel. "I played it very cool. Then I called my girlfriends: 'Ladies, he's friends with Jon Hamm. Shut the front door.'

As her relationship progressed, Rose said, "I started asking questions like, 'What's Jon like? Will he be there? And he would just say how lovely he was and how funny he is, which you probably don't always associate with Jon because of Mad Men and being such an intense portrayal."

Marriage has always been important to Rose, and she wants the LGBTQ community in her native Australia to experience all it has to offer. "#sayidodownunder my lady wants you to know she's in favor of her home country joining the rest of the enlightened world in giving people the right to choose whomever they want to marry," Bobby wrote in an Instagram caption three weeks ago. "Spread the above hashtag if you feel the same. Ain't she cute?!"