The "Bridesmaids" star has been in a relationship with "The Irishman" actor since 2012, and although they have never publicly discussed a formal engagement, Byrne reveals they've had the discussion about tying the knot for some time.
However, they kept postponing the idea as they became parents to sons Rocco, five, and Rafa, three, and when a gap in their schedules eventually opened up, they had no choice but to put the marriage talk on hold again due to the coronavirus crisis.
Asked about the possibility of becoming husband and wife, Byrne told The Sunday Times Style magazine, "I keep going, 'Let's get around to it, let's do it,' and then, you know, you have a baby, and then, oh, there was another baby. It was kind of like that for us."
"I love weddings, and I know people [for whom] it's an important thing, and I respect that totally," she continued. "I guess for us it's just been, we didn't do it, we'll do it, then - no! Pandemic."
The actress and her family left their home in Brooklyn, New York to spend time in her native Australia in the early days of the shutdown, and she recalls how unsettling their final days in the U.S. were.
"It was scary, trying to figure out how to get out and be safe. And no one knew anything, right? We were all in this boat of, 'What is this?' It was a very, very weird atmosphere in the city," she shared.
"Bobby and I went to see 'Girl from the North Country' on Broadway and then, two days later, Broadway shut, and by that weekend it was awful.
"All of a sudden there was this tsunami, tidal wave, of this fearsome thing coming, and then it just arrived and it was like, whoa. Then people we knew started to get it. Bobby lost friends."
It appears the stars are still camped out Down Under, but it won't be that way forever.
Rose added, "Brooklyn is home."