Spanish magazine Hola!, which broke the news of the birth of the couple's first child in February and published exclusive photos of their May 2018 wedding near New York, says the baby is expected in "next spring", reports dailymail.co.uk.
The "Pretty Woman" star Gere, who turned 70 at the end of August, also has a son aged 19, Homer James Jigme Gere, with former wife Carey Lowell.
Alejandra, 36, who was born in Spain's northwest region of Galicia, is mother to a six-year-old son called Albert with her ex-husband Govind Freidland.
Alejandra confirmed her first pregnancy in September last year after marrying Gere with a photograph showing the Dalai Lama touching her belly in a blessing, a month after it was revealed she was expecting.
The news she was pregnant emerged just six months after she tied the knot with her actor partner at a civil ceremony in Spain before celebrating the occasion with friends and family at Gere's home near New York.
Gere told Hola! in an exclusive interview after the wedding: "I'm the happiest man in the universe and how couldn't I be! I'm married to a beautiful, sensitive, funny woman who's committed to helping people and is a great mother."
( With inputs from IANS )