St Joseph’s Home for Girls, closed in 1973 and the building later became a school for deaf children known as St Vincent’s.
Further down the line the premises, on Church Street, became an independent Christian school for seven to 18-year-olds, but that closed too, in 2014.
Now developers McCarthy and Stone want to convert the empty building into a 51-apartment complex for elderly people.
Among the communal features built under the scheme would be a lounge, mobility scooter store, and gardens, including a terrace.
There would also be 37 parking spaces on the site for residents.
In a planning statement submitted to Leeds City Council last week, McCarthy and Stone said the scheme presented an “ideal opportunity” for redevelopment of a brownfield site.
They added: “It would also provide much needed specialised housing for the frail elderly within a central location, therefore helping to prevent new housing on green belt land and to free up existing underoccupied stock.
“This specialised form of housing provides the frail elderly with a better housing choice.
“It provides residents with safety, support, security and companionship and removes the heavy burden of property maintenance.
“Therefore, it reduces the anxieties and worries experienced by many elderly people living in accommodation that does not best suit their needs.”
The developers also said the scheme will benefit the local community because residents will make use of the nearby amenities, shops and post offices.