Moore also told E! Online she supports Page's decision to come out. Page made the announcement at a recent Human Rights Campaign event in Las Vegas.
"It was really wonderful," Moore said at a premiere for her new movie, "Non-Stop," which opens in theaters Friday. "I was very happy for her."
Moore said she is "excited" about "Freehold." The movie, based on fact, is about a dying police officer unable to assign pension benefits to her partner.
A campaigner for gay rights, Moore lives in New York City with her husband, director Bart Freundlich, and their two children. Page, 27, is Canadian and is best-known for playing a pregnant teenager in the 2007 film "Juno."