Weinstein's second wife, fashion designer Georgina Chapman, is pregnant with the couple's second child, reported Express online.
Weinstein already has a two-year-old daughter India Pearl with Chapman.
"We are both over the moon," while Weinstein adds, "We don't know the sex, it could be Harvey and five daughters. I'd be happy either way," Chapman said.
The producer has three daughters, Lily, 17, Emma, 14, and Ruth, 10, with ex-wife Eve Chilton, whom he divorced in 2004 after seven years of marriage.