Modern-day Iran is nowhere near India. True. However, modern-day borders are often only tangentially related to the great empires of old. The Roman republic and empire spread further than modern Italy. India used to be balkanised into many different independent states. Pharaonic Egypt at various moments in time ruled as far south as most of Sudan, and as far north as Lebanon. Turkey is a mere shadow of the Ottoman Empire, whch ruled pretty much the entire Middle East and the Balkans for centuries. Achaemenid and Sassanid Persia, the two great Persian empires, were much, much larger than Iran is today. The Achaemenid empire especially is one of the largest empires in the world (IIRC not in the top-whatever, but still significant enough to be worth mentioning). Their lands stretched from Anatolia (Turkey) to the Sinai (and IIRC they occupied Egypt at some point too), north to the Caucasus and Central Asia (now home to a gaggle of tiny post-Soviet states) to the Indian Subcontinent. The Persian empires, be they Achaemenid, Sassanid, Hellenistic Seleucid or any I'm forgetting, always had close ties to India, and trade (and warfare) was rife. The pride of the Persian armies were the war elephants, imported from India (and often with Indian handlers to boot).
Even disregarding the common border on land, trade and other contact would be very much possible by sea. There's a reason it's called the Persian Gulf - and it opens into the Indian ocean. Coastal trade was very common since long before the Achaemenids, and it remained a major factor for long after the Sassanids. Persian, Arabian, Indian and even Chinese traders made the Indian Ocean a hotbed of commerce, connecting everything from the African East Coast to the Pacific in one giant interwoven web of trade.
One other constant factor of the various Persian and Arabian empires, right up until about the nineteenth and twentieth centuries, was a very tolerant cosmopolitanism, and people from various races and various geographical backgrounds could become rich and powerful on their own merit. So an Indian vizier, or at least one of Indian descent with visible Indian traits, is a distinct possibility.
Just my ?0.02 on the matter of historical relations. It's kind of my thing. It's amazing how little people actually know about history, and even more amazing that they don't realise just how little they actually know even if they're aware of it. But that's a whole different rant.