The Bridesmaids star is currently appearing in a Sydney production of David Mamet's Speed-the-Plow play in her native Australia, and she was recently spotted out and about with a new diamond sparkler on her left ring finger.
Representatives for Rose, 37, and Bobby, 46, have yet to comment on the speculation.
If the engagement news is true, it shouldn't come as much of a surprise to fans as the couple, which began dating in 2012, welcomed its first child together, son Rocco, in February (16).
The actress recently opened up about adjusting to life as a new mum, admitting she rarely left home in the first few months after Rocco's birth because she was so exhausted.
"I'm still in a fog," she laughed to news.com.au in May (16). "I haven't even left my apartment in three months."
"I'm tired, but even so, all of it's great," she gushed about motherhood. "But you definitely go into a cocoon. Sleep is what makes me feel good at the moment, wherever I can squeeze it in that's the best thing for now."
Rose also revealed she was grateful to have Bobby by her side as she has learned a great deal about parenting from the Boardwalk Empire star.
"He's terrific," she smiled. "He has a 21-year old (from a former marriage) so this is old hat to him. And I have to say, having someone who's already a parent is great because this is all very, very new to me. So I'm just taking tips from him."