Dear Ms. Griffin,
Thank you for posting your request on History Hub!
We suggest that you submit a Name Index Search to the US Customs and Immigration Service (USCIS) to obtain a copy of your great grandfather’s records. If he did not complete the process, USCIS should be able to provide the certification on non-existence, and although your great grandfather won’t have a naturalization record, it is likely that INS did create a file that could be used to verify his citizenship status.
We hope this is helpful. Best of luck with your family research!