Via NRO:

The caliph of the newly established “Islamic State” in Syria and Iraq is already looking to expand the territory in to the West. […]

Additionally, Baghdadi predicts that following his advice will lead to the growth of the Islamic State. “If you hold to it you will conquer Rome and own the world, if Allah wills,” he said.

Past caliphates have fallen short in conquering Rome, although at its furthest extent, the Umayyad Caliphate of the seventh century included parts of Europe, occupying most of the Iberian Peninsula and reaching parts of France.