It is like asking if someone can build a church inside the Great Mosque of Mecca. The Great Mosque is roughly 36 hectares, and the Vatican City-State 44. They are close to the same size. read more
To put a mosque in the Vatican would be as silly as putting a synagogue in Mecca’s Grand Mosque, because 1) there’s not enough room & 2) neither would get used (since Vatican citizens are Catholic & Mecca does not allow non-Muslims inside the city). read more