Martinez, who met 45-year-old Berry on the film “Dark Tide” in 2010, gave her a diamond-and-emerald engagement ring, the celebrity bible reported, citing a jeweler’s publicist.
The French star is the former partner of Australian superstar Kylie Minogue. He and Berry were most recently spotted at Canadian dance troupe Cirque du Soleil’s show “Iris” at the Kodak Theatre in Hollywood.
Berry has been married twice before, to baseball player David Justice and singer Eric Benet, and has a 3-year-old daughter Nahla with ex-boyfriend Gabriel Aubry.
The actress’s publicist did not respond to a request for comment or confirmation of the People story, which was also reported by the US Weekly magazine.
Berry, famous for the “X-Men” movies and as a Bond girl in “Die Another Day,” won a coveted best actress Oscar in 2002 for her turn in “Monster’s Ball,” the first such award to an African American actress.