"They tried to keep it very private and quiet," the source continues of the couple, who began dating in 2007. (They first met while filming flick Jamon, Jamon in 1992.)
A rep for Cruz, 35, had no comment.andnbsp;
A pal told the New York Daily News, which first reported the story, that Cruz wanted to wed Bardem, 40, to appease Cruz's Catholic parents -- given the persistent rumors that she's pregnant, which she's denied.
Cruz once said she wasn't sure she wanted to be a wife.
"I don't know if I believe in marriage," she told Psychology Today in August. "I believe in family, love and children."
She continued: "When I [have children], I want to do it really well. I want it to be my best project in life."