Live music, drama, visual art and poetry events would take place throughout the A-listed landmark building if the Hidden Door Festival is held there.
It is about to breathe new life into the former Leith Theatre building almost 30 years after it last hosted any events.
Organisers of the festival, which is usually staged in empty buildings ahead of redevelopments being carried out, said the hospital building was top of its list to try to take over in future.
Designed by architect David Bryce, the 19th-century surgical hospital building had been expected to become a new luxury hotel as part of the transformation of the former Edinburgh Royal Infirmary campus, which was sold to a developer in 2001, two years before the relocation of the hospital to Little France, but has only been partly redeveloped.
The building, which dates back to 1879, was bought by Edinburgh University at the end of 2015 from the current developers behind the “Quartermile” project.
The university plans to create a teaching campus for humanities, business and arts disciplines, but full details have yet to be revealed.
When the purchase of the building was announced in 2015, principal Sir Timothy O’Shea said: “It will enable us to expand our outstanding teaching facilities and help consolidate our position as a world-class university that is accessible to the wider community.”
O’Shea, who steps down from his post in September, has been chair of the Edinburgh Festival Fringe since 2012 and was appointed for a second term in November 2016. The university has extensive involvement in many of the city’s festivals, hosting and sponsoring events.
Hidden Door has previously deployed Victorian arches on Market Street and an old council lighting depot on King’s Stables Road.
Creative director David Martin said: “There is more space around the city than the general public thinks. The old surgical hospital is a huge part of the Quartermile development which is lying closed and derelict. That would be my top mouth-watering choice for Hidden Door. I hope to get a meeting with the university about it.
“We want to do better and more interesting things. Our problem is we can’t plan ahead very far. The nature of empty buildings means that people don’t want them empty for very long.”
A university spokeswoman said: “We’ve not received a formal approach from Hidden Door Festival, but we’re always happy to explore any new proposals that involve working with the city’s cultural organisations.”