People confirmed the 30-year-old American actress is having a baby with Wright, 46, who is known for directing such films as Pride & Prejudice, Atonement and Darkest Hour.
Page Six reported Bennett is about six months along in her pregnancy. Sources said Wright has moved to the U.S. to be with the actress.
"They're expecting a baby this winter," an insider said. "They are very happy."
Bennett has yet to confirm the news on social media, but posted a cozy photo of herself reading in bed Tuesday.
"Once Upon a Time..." she captioned the picture.
Wright is already parent to two sons, 7-year-old Zubin and 3-year-old Mohan, with ex-wife Anoushka Shankar. Bennett confirmed her relationship with Wright in September following the director's split from Shankar in June.
"Cling to me, Joe, my bliss," she captioned a photo of herself kissing Wright.
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Bennett is known for the films Music and Lyrics, Hardcore Henry and The Girl on the Train. She will appear in the movie The Red Sea Diving Resort with Chris Evans and Swallow with Austin Stowell.
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