The Turks wouldn't mind, would they?
As a matter of fact, I was once in a tour group going through the Hagia Sophia. The group included a couple from Saudi Arabia. The man asked the tour guide if they could pray there. She told them no, they couldn't, they should wait until we got to the Blue Mosque, later on our tour. So I guess the Turks would mind. Unless you prayed silently while standing.
Strange that these Muslims thought to pray in the Cathedral of Our Lady of the Assumption when their brothers and sisters in London have been protesting for months now demanding their own private prayer space at City University. These British students claim that Muslims cannot pray in any location which is shared with prayers of other religions.
How were these Austrian tourists left out of the loop?
—We have been moved out of our prayer room, located near the Social Sciences building, to the dungeons of the main university building. A place with naked men to glance at whilst performing wudhu, a place unsuitable to provide for our large number and a place that allows the worship of that other than the One True God.
http://citymuslims.co.uk/?page_id=4