Are there any Muslims in Vatican City?

There is currently no mosque in Vatican City. There is no synagogue or pagoda either. There is not even an airport (there is a heliport), stadium (even though they have a national soccer team), kindergarten or school (even though there are kids), or McDonald's (people in Vatican City need to eat too). For the most part, they have access to those facilities outside the city walls, in the territory of the Italian Republic.

It should be noted that there is no ban on building mosque or pagoda or stadium. The real problem, however, is that you can't actually find a plot of land to build it. Vatican City is basically comprised of a tiny walled estate, and nothing else. The use of land has already been highly optimised, due to the limited building area. Moreover, there is no public land available; all lands are private property of the Holy See (which is a distinct entity from the Vatican City State), and none is for sale; with the extremely lack of land for their own use, I don't think the current owner is willing to transfer ownership unless there is a strongly compelling reason.
Last but not least, a mosque is obviously not a top priority in Vatican City, as there is practically no Muslim resident inside its city walls for it to serve. Muslims residing in Rome, on the other hand, are served by the Mosque of Rome, the largest mosque in Europe (which is about 6km from St Peter's Basilica).

So, it can be said that assumably, all the Muslims in the Vatican City are just tourists who have come to visit it and virtually, no Muslims reside in the Vatican City.

Vatican City is the smallest independent state in the world and the spiritual and administrative center of the Roman Catholic Church. The majority of the population in Vatican City consists of clergy, including priests, cardinals, and other religious officials. As of my last knowledge update in January 2022, the population of Vatican City is predominantly Catholic.

Muslims, like followers of other religions, are generally not considered residents of Vatican City as it primarily serves as the headquarters of the Catholic Church. However, Vatican City, like any other place, may have visitors from diverse backgrounds, including Muslims, who come for tourism or other purposes and small numbers who live there.

The population of Muslims in Vatican City in 2010 was estimated to be under 1,000 people comprising approximately < 0.1% of the population of the state.

The projected population for 2030 remains less than 1,000 comprising less than 0.1% of the state. There are also no mosques reported to exist in Vatican City.

Source: Pew Research Religion and Public Life Project