Whichever, all eyes were on the Spanish star at the premiere of director Pedro Almódovar's Broken Embraces on Sunday's closing night of the 47th New York Film Festival at Lincoln Center, where Cruz, 35, wore what appeared to be a knuckle-sized sapphire surrounded by small diamonds on her ring finger.
"She has achieved a very handsome, good boyfriend, two Oscar nominations, one Oscar and the respect and admiration of her profession," Almódovar, 60, said.
But Cruz didn't speak about what, if anything, the ring signifies, preferring instead to talk about Almódovar's generosity to his actors rather than boyfriend Javier Bardem's generosity with jewelry. (A source close to the actress also declined to address the ring's significance.)
"Pedro and I have been friends since I was a kid," said Cruz. "We spent three months finding the characters. That's very generous of him, very rare."
"She's emotional in general … in her life," Almódovar told PEOPLE. "Between takes, during takes … The sentiments were coming freely about the character, so I had to dry many tears in this movie with her."
PeopleTV Archive: Penelope Cruz on her important pre-Oscar stop