According to the paper, neighbours became suspicious before complaining about irregular behaviour of those coming and going at the apartment.
When police showed up at the apartment, they reportedly found drugs and a group of men engaged in sexual activity.
The priest was then arrested and taken for questioning.
Il Fatto Quotidiano suggested that Pope Francis was infuriated by the news and may force Coccopalmerio into retirement.
The alleged orgy is symptomatic of a difficult period for the Pope. Four years into his papacy the Catholic Church appears racked by conflict and scandal.
Critics blame the Pope's choice of personnel: cardinal George Pell, appointed to clean up the Vatican's murky finances, has taken a leave of absence to defend himself against sex abuse charges in Australia.