But, adhering to the recently married couple's tradition of keeping mum about private matters, Bardem, 41, added: "Don't make me say anything else."
Not that this request prevented journalists at a press conference in Rome for the leading man's movie with Julia Roberts, Eat Pray Love, from pressing ahead with questions about Baby Bardem.
Has a name been chosen for the impending arrival, asked a reporter for a national Italian newspaper. "No, not yet," replied Bardem.
The key to managing a family and a career? "It is a little too soon for me to be giving any advice," said the actor. "I don't know yet. But I will find out soon."
Finally, when one journalist asked what it felt like being a sex symbol, Bardem replied modestly, "Sex symbol, me? You've got to be kidding."