The Spanish actors, who were first linked this summer, were photographed relaxing together in the Maldives this month. They were also filmed hugging in New York in this video.
Cruz, who dated Tom Cruise for several years, has been fielding questions about Bardem for some time. This summer, she was asked about rumors of a courtship. "It's not true," she replied at the time. "He's a friend and the best actor in the world."
Earlier this week, the New York Post's Page Six reported that the pair were spotted being "very touchy-feely."
Bardem earned a best-actor Oscar nomination in 2001 for Before Night Falls. Cruz picked up a best-actress nomination this year for Volver. Bardem is currently promoting his new film, No Country for Old Men.
Calls to reps for both actors were not immediately returned.