Slop.

Near east was anything west of the Persian gulf that wasn't the west, middle east was anything east of it until we got to the far east.

The "Near east" would include the Arabian peninsula, Iraq, Iran, the Levant, Cyprus and Egypt.
So yeah "Ottoman Empire" if you're extremely generous

To quote wikipedia

According to the National Geographic Society, the terms Near East and Middle East denote the same territories and are "generally accepted as comprising the countries of the Arabian Peninsula, Cyprus, Egypt, Iraq, Iran, Israel, Jordan, Lebanon, Palestinian territories, Syria, and Turkey".[6]

And

The term Near East was used to refer to the part of the Orient nearest to Europe, as opposed to the Middle East (then comprising the lands between the Persian Gulf and Southeast Asia)[3] and the Far East (East Asia and beyond), together known as the "three Easts";