Reynolds and Lively, who have been married since 2012, already have two daughters: James Reynolds, 4, and Inez Reynolds, 2.
The couple are notoriously private and earlier this year Reynolds opened up to Fatherly.com about his decision to keep his children out of the spotlight.
"We live as normal a life as we can live," he said. "Our kids aren't a part of Instagram or social media. I talk about them, but I never post photos of them and neither has Blake. It's not something we would want to be a part of.
"Being in public is a choice that people should be allowed to make when they're of age. I would never want them to resent me for that. I want them to have as normal a childhood as possible."
Despite not sharing photos of them, Reynolds is famous for making jokes about his kids. After his first child was born, he told talk show host David Letterman: "I used to say to (Blake), 'I would take a bullet for you. I could never love anything as much as I love you.' I would say that to my wife. And the second I looked in that baby's eyes, I knew in that exact moment that if we were ever under attack, I would use my wife as a human shield to protect that baby."
Reynolds, whose latest movie 6 Underground will be released on Netflix on December 13, has also delighted fans over the years with his hilarious tweets about fatherhood.
Here are some of his best tweets:
