The drugs were found at Leipzig airport, Germany, in January and were hidden in a shipment of cushions sent from South America, Bild newspaper reported.
Officials are unsure who the 340g (12oz) of cocaine was meant for as the packages were addressed to the Vatican postal office.
This meant they could be picked up by any one of 800 residents.
Bild added a German customs report showed a sting operation organised with Vatican police failed to identify a possible recipient.
The drugs are said to have a street value of several tens of thousands of pounds.
The Vatican and German customs officials have yet to officially comment on the report.