The comments follow media reports alleging how hundreds of millions of dollars from the two companies were used for illicit payments.
A joint investigation by BuzzFeed News and Italian newspaper Il Sole 24 Ore on Sunday claims to show transactions worth $1.3 billion made in 2010-2011 that Shell and Eni paid to acquire an exploration licence for an offshore oil block known as OPL 245.
The money was paid to the Nigerian government, but BuzzFeed and Il Sole said documents showed Shell's top executives at the time knew those sums would go to Malabu Oil and Gas, a front company connected to former Nigerian oil minister Dan Etete.
Attempts by Reuters to contact Etete have been unsuccessful.
In emailed comments, an Eni spokesman said the allegations in the reports were not supported by the facts, the underlying agreements or the independent investigations conducted to date.
"Neither Eni nor Shell paid any monies other than as contemplated and recorded by the Block Resolution Agreement and did not pay to Malabu, to Chief Dan Etete or to any public officer," the spokesman said.
Shell said that "based on our review of the Prosecutor of Milan's file and all of the information and facts available to Shell, we do not believe that there is a basis to prosecute Shell. Furthermore, we are not aware of any evidence to support a case against any former or current Shell employee".
In an emailed statement, Shell added that if the evidence proves improper payments were made, "it is Shell's position that none of those payments were made with its knowledge, authorization or on its behalf".
Courts in Nigeria and Milan are investigating the 2011 purchase of the block, which industry figures suggest could hold more than 9 billion barrels of oil.
Italian prosecutors are working with an anti-fraud team in the Netherlands that raided Shell's The Hague headquarters in February 2016 in relation to the investigation. A Nigerian court ordered the asset temporarily seized in January at the request of Nigeria's Economic and Financial Crimes Commission, but the seizure was later overturned.