The article, published in the latest edition of the magazine, reports that the Home Alone star has a $6,000-(£3,835)-a-month drug habit, and also regularly takes the painkiller oxycodone recreationally.
It also states that Culkin invites friends into his Manhattan apartment to take drugs together, and that his addiction intensified after his split from former girlfriend Mila Kunis in 2011.
A representative for the actor denied the claims on Wednesday (August 1), saying that the Enquirer's report is "destructive and insulting", and that the story is "not only categorically without merit, but it is also impossibly and ridiculously fictitious".
However, the magazine has since gone on to offer an official statement, published on Friday (August 3), saying that it hopes the report will act as "a dramatic and much-needed wake-up call" to the 31-year-old.
It went on: "We believe that the former child star should be doing everything he can to get the treatment he so desperately needs - and which could have saved the life of his friend Elijah Rosello. Her family confirmed to the Enquirer that she did drugs with Macaulay before her drug-related death in March.
"Should Macaulay's representatives continue to deny the Enquirer's accurate and detailed report, we are ready to offer him the opportunity to take a blood test administered by an independent medical lab."
Culkin sparked concern after being pictured having lost a dramatic amount of weight in February. At the time, his representative said that he was in "perfectly good health", and that media reports suggesting otherwise were "reckless, irresponsible and destructive".