Reed, who the magazine said passed away on Sunday, had undergone a liver transplant in May.
Born in New York in 1942, Reed found success with legendary 1960s band the Velvet Underground and produced music that influenced generations of musicians.
After leaving the band in 1970, he embarked on a solo career during which time he released the David Bowie-produced album Transformer and was thrust into rock superstardom.
Reed recently had a number of health problems but was hopeful.
"I am a triumph of modern medicine, physics and chemistry," he wrote on the social media. "I am bigger and stronger than stronger than ever."
The magazine gave scant details about the death, and Reed's representatives could not immediately be reached to confirm the news.
