The unidentified woman recently filed a police report accusing Green of sexual battery.
TMZ said the woman told police she had a drink with Green at a downtown Los Angeles restaurant in July, and then woke up naked with the recording artist the next morning, having no further recollection of the previous night.
The alleged victim does not live in California and almost immediately went to her local law enforcement agency to report the incident, the celebrity news website said.
The matter was referred to the Los Angeles Police Department, where detectives recorded a call from the woman to Green, during which they discussed the events of the night in question, TMZ said.
The website quoted sources who heard the audio as saying Green repeatedly apologized for his behavior. The insiders said he referred to ecstasy, although he did not specifically say he put the drug in her drink.
Green, a star of TV's "The Voice," has denied the allegations to the media and no criminal charges have been filed.
Green will soon be seen in a holiday special co-starring The Muppets.