But with the decision to turn the museum into a mosque, Turks have been wondering whether Gli will have to move out -- with the question cropping up daily on local news outlets and social media.
The grey cat with shining green, crossed eyes, has become a favourite with visitors, including former U.S. President Barack Obama, who was filmed stroking her during a trip in 2009.
Authorities have made clear Hagia Sophia can remain as her home.
Ibrahim Kalin, spokesman for President Tayyip Erdogan, told Reuters that Gli, as well as all other cats in the area, would stay where they were.
"That cat has become very famous, and there are others who haven't become that famous yet. That cat will be there, and all cats are welcome to our mosques," he said.
That's bound to be welcome news to Umut Bahceci, a tour guide who started an Instagram account for Gli four years ago and now has more than 48,000 followers. The account is filled with photos of the cat, some tagged by the tourists who meet her.
"I started noticing Gli every time I went (to Hagia Sophia) because Gli was posing for people like a model," she told Reuters. "I get messages such as, 'Gli, we will come to Istanbul to see you.' This is truly a very nice feeling,"
Hagia Sophia was a Christian Byzantine cathedral for 900 years before it was seized by Ottoman conquerors and served as a mosque until 1934.
A court ruled this month that the building's conversion to a museum then was unlawful. Erdogan immediately declared the building a mosque once more, with the first prayers to be held this Friday.
