The Hollywood actor branded the Mail Online at the "very least negligent and more appropriately dangerous" for the story and said he felt compelled to respond because "it involves someone else and their safety or well-being."
The website apologised to Clooney claiming they were given the story by a "reputable and trusted" freelance journalist.
Clooney has since rejected the Mail Online's apology.
Writing in the USA Today, he said: "I thank the Mail for its apology. Not that I would ever accept it, but because in doing so they've exposed themselves as the worst kind of tabloid.
"One that makes up its facts to the detriment of its readers and to all the publications that blindly reprint them."
Meanwhile, fellow Hollywood star Angelina Jolie is to sue the Daily Mail after it published a video online which claims to show her addicted to heroin during the 1990s, according to The Times.
The 16-minute footage was allegedly filmed by Franklin Meyer, who claims to have been her drug dealer when she was living in New York.
In it the actress walks around her apartment on her phone allegedly talking to her actor father Jon Voight about her brother James and her late mother Marcheline Bertrand.
The actress has been open about her drug-taking past but is said to believe the publication of the video is a "gross violation of her privacy."