The All The Pretty Horses actress and her Skyfall actor husband Javier Bardem are thought to be expecting a sibling for their two-year-old son Leonardo, according to the New York Post's Page Six.
The couple - who had been friends for years - started dating in 2007 and married in early July 2010 in an intimate ceremony at a friend's home in the Bahamas.
Penelope, 43, has previously spoken out about how motherhood has transformed her life.
She said: "From the first second, you feel so much love.
"It is a revolutionary experience. That's the best way I can describe it. It transforms you completely, in a second. Nature is very wise and gives you nine months to prepare, but in that moment, when you see that face, you are transformed forever."
She is also determined to keep her kids out of the public eye, despite hers and 43-year-old Javier's successful careers.
She explained: "I want my son and my kids - if I have more - to grow up in a way that is as anonymous as possible.
"The fact that his father and I have chosen to do the work we do doesn't give anybody the right to invade our privacy."