Hutchesons' Hall, in the Merchant City and which is owned by the National Trust for Scotland, has been sitting empty since January 2008.
But now the organisation has submitted an application to the city council asking to change its use to a restaurant.
A spokesman said: "The Trust has been working hard to find a tenant for this wonderful building over the past few years.
"We are in discussions with a prospective tenant, hence the change of use application. Negotiations and discussions are under way."
Hutchesons' Hall, in Ingram Street, was built in the early 1800s by David Hamilton.
It is named after the Hutcheson brothers, George and Thomas, whose statues adorn the front of the building.
The statues were created in the 17th Century and were originally on the first Hutchesons' Hospital, in Trongate.
Although Hutchesons' Hall was meant to be a hospital for the elderly, it was never used as such.
Instead, it has been used as a public library, bank, school and shops.
The A Listed building features an impressive clock tower in an unusual octagonal design.
The National Trust for Scotland bought Hutchesons' Hall in 1982 as a base for staff and it was later used for small exhibitions, functions and retail.
It closed five years ago after sustaining significant damage in a winter storm.
Since then, the Trust has carried out a series of external repair works in the hope of finding a tenant.
Thomas Hutcheson, who was born in 1590, was a philanthropic lawyer whose older brother George had left money in his will to build Hutchesons' Hospital as a hospice for poor old men.
Thomas provided cash for Hutchesons' Grammar School for orphaned and under-privileged boys, which was originally housed in the hospital building.