The celebrity news Web site did not say when Paquin is due to give birth or what the gender of the baby is.
The couple began working together in 2007 and married in 2010. Moyer has a son and daughter from previous relationships.
Paquin won a supporting actress Oscar for "The Piano" in 1993.
LGBT community has 'bullied the American people': Bachmann
Astronomers offer more expansive view of universe