The pair were recently observed embracing while attending the premiere of Killing Them Softly in New York City, according to Us Weekly.
A source close to Cannavale has since told the publication: "They've been dating for a few months. I think Rose is a good match for him."
Representatives for Byrne and Cannavale have not commented on the dating rumours.
Damages star Byrne famously dated Australian actor-director Brendan Cowell for several years. She was also in a relationship with her Two Hands filmmaker Gregor Jordan.
Cannavale was married to iconic director Sidney Lumet's daughter Jenny Lumet from 1994 to 2003.