My say is that it was practically impossible, but if anybody had a mouse's fart of a chance it's the Umayyad Caliphate with all of its resources and vast armies. If the Caliphate had decided for some reason to abandon Persia for the riches of the Byzantine Empire, or perhaps liberalizing and not treating Arabs specially, then they would have faced less unrest within their territories. Once Anatolia and Greece were conquered, they would of course be tempted to roll into Italy, or at least Sicily, unprotected as they are (relatively) from naval invasions. The Iberian coast is a bit harder to get and the French very hard without full conquest of Spain, but either way I see them getting 80% of the shoreline by the 1500's...provided that they are very lucky.
But hey, if Alexander happened I think anything is fair game.