The couple have remained mum about their new son's name since Cruz gave birth in Los Angeles on Jan. 22. However, Spanish film director Santiago Segura referred to the baby as "Leo" when chastising a group of reporters, according to Spanish media reports.
"I know what you want and you don't understand why they don't come running to show off the baby and say, 'Look, here's Leo,' " Segura reportedly told reporters when discussing the press-shy couple.
When pressed about the name, Segura reportedly replied, "Yeah, Leo. I think so. That's what I think I heard. But they haven't said anything."
The Spanish lovebirds quietly married last July and are notoriously private.
Reps for the actors were not immediately available for comment.