FamilySearch.org has a FREE database titled UNITED STATES PASSPORT APPLICATIONS, 1795-1925 that includes 4,518 people born in Greece.
You will be able to view actual copies of the passport applications.
Note: On December 24, 2014 I made a post based on the Ancestry.com database "United States Passport Applications, 1795-1925". This database contained 7,725 people born in Greece. The database mentioned in my current post may be a sub-set of the records contained in Ancestry.com's.
This collection contains United States Passport Applications from two different NARA collections: M1490, and M1372. This collection is currently being indexed and the indexed records are being published.