Byrne, 37, was spotted out and about in her native Australia last week, wearing a stunning rock — hinting that the pair are planning nuptials. The square-cut bling appears to be white gold and feature a halo of diamonds. Reps for the pair have not commented on a possible engagement.
The couple, who have been dating for over four years, are parents to son Rocco, 9 months.
The Vinyl star and Byrne not only share a life offscreen, but have also appeared together onscreen in Annie, Spy and Adult Beginners. Mixing personal with the professional “is a very intense thing you can experience together,” Byrne told PEOPLE in 2015. “It’s not for everybody, but I think he’s such a great actor.”
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And Cannavale’s acting wasn’t all that stole Byrne’s heart: he’s also a “great cook,” she said.
“He’s Cuban and he does a couple of really good Cuban dishes like arroz con pollo and Cuban cocktail,” Byrne gushed of Cannavale, 46. “He’s better than I am. I’m the good cleaner after!”