It is highly unlikely that your great grand parents would have notified the Italian consulate of their acquisition of citizenship. You need to do your search in US records. Begin with ancestry.com. That may point you in the right direction.
If you have checked all the naturalization options (at the national and county levels) and find no record of naturalization, they did not naturalize.
If your search is for citizenship purposes, you will have to obtain letters of no record to support your claim. Your consulate will also likely request supporting census data, so that is another search you should initiate on the ancestry site.
Have you checked the census records? They will show whether he identified himself as naturalized or alien.
Information from family members is helpful but not always accurate. If there is no naturalization record anywhere, he didn't naturalize.
One other possibility is that your great-grandparents naturalized as minors with their fathers. If so, the naturalization records would not be in their names. Is it possible they came to the US when they were children.
Here is where you can make a search for Naturalization records - this is the Genealogy section of the USCIS. If anyone of your relatives went through the Naturalization process in America, they will have a record of it and supply you with a letter and copy of the certificate. That will suffice for your application.
If your GGM was alive in the early 1940s, you can also check with NARA at the address Phil posted above and order a copy of her Alien Registration Form. My dad was convinced that his grandparents naturalized, but these definitively showed they did not!