The Roman Empire which represent the two legs of iron on the image in Nebuchadnezzar's dream consisted of both the Eastern Empire and the Western Empire. So I don't see why the feet and 10 toes of iron mixed with miry clay on the image couldn't represent an Islamic beast kingdom since the Eastern Part of the Roman Empire at its greatest extent in 117 A.D. contained the countries of Turkey, part of Arabia, part of Iraq, Lebanon, Syria, Egypt, Israel, Armenia and Albania.  There are also a lot of Muslims living today in Europe in the countries that once made up the Western part of the Roman Empire. So I don't see why they couldn't be an Islamic beast kingdom that comes from the Roman empire.

Constantinople (now Istanbul) became the capitol of the Roman Empire in 330 after Constantine the Great refounded the city of Byzantium and renamed it after himself. The Byzantine Empire was the Eastern part of the Roman Empire, which survived after the breakup of the Western Roman Empire in 5th century A.D. when roving Germanic tribes removed the last emperor Romulus Augustulus in 476 A.D. The Ottoman Turks conquered the remnant of the Byzantine Asia Minor early in the 14th century bringing the Empire to an end in 1453 A.D.