The Avengers actress has yet to comment on the speculation, but fans spotted her wearing a stunning diamond ring while at the Venice Film Festival 2013 this week.
Scarlett, 28, was there to promote her new movie Under The Skin, and wowed at its glitzy red carpet premiere in an old Hollywood-style black gown and sultry make-up.
A source told People that the engagement happened about a month ago and that Scarlett is, understandably, thrilled.
Romain joined Scarlett in Venice this week, attending her premiere looking very handsome in a tuxedo. At one point he was caught gazing at her inside the cinema.
It's been claimed that Scarlett and French journalist Romain met via a mutual friend nine months ago.
Scarlett has been married once before, to actor Ryan Reynolds. They separated in December 2010 following two years of marriage.
More engaged celebrities on our gallery below!
Copyright: Instagram Mark Wright