The 60-year-old actor has twins with his wife, Amal, 43: Ella and Alexander, both four.
Now, in a letter published by several trade magazines, including Deadline and The Hollywood Reporter, Clooney has addressed “the Daily Mail and other publications”, calling on them to protect his children’s privacy.
The letter began by addressing photographs of US actor Billie Lourd’s one-year-old daughter that had been published online.
“Having just seen photos of Billie Lourd’s one-year-old baby in your publication, and the fact that you subsequently took those pictures down, we would request that you refrain from putting our children’s faces in your publication,” Clooney wrote.
“I am a public figure and accept the oftentimes intrusive photos as part of the price to pay for doing my job. Our children have made no such commitment.
“The nature of my wife’s work has her confronting and putting on trial terrorist groups and we take as much precaution as we can to keep our family safe. We cannot protect our children if any publication puts their faces on their cover.”
The Ocean’s Eleven and Gravity star continued: “We have never sold a picture of our kids, we are not on social media and never post pictures because to do so would put their lives in jeopardy. Not paranoid jeopardy but real world issues, with real-world consequences.
“We hope that you would agree that the need to sell advertisement isn’t greater than the need to keep innocent children from being targeted.
“Thank you, George Clooney.”
The Daily Mail has not yet responded to the letter; The Independent has contacted the publication for comment.
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