The Lace Centre opened in 1980
An architectural historian has said more should be done to preserve Nottingham's old buildings and medieval history.
The call came as Nottingham's Lace Centre shut its doors for the last time on Tuesday and follows the closure of several historic attractions.
The centre, which showcased the city's famous lace industry, has left the Grade II listed Severns building empty.
Historians said the 14th Century site is one of the city's most important.
Ian Wheeler, an architectural historian and a member of Nottingham's Civic Society, said: "It is one of the few buildings surviving from the old town of Nottingham.
"It is very important in architectural and construction history."
Mr Wheeler said he was keen for Nottingham's history to be preserved following the closure of attractions such as the Tales of Robin Hood and the uncertain future of the Industrial Museum.
He said: "It is very worrying. There have been other threats, the Industrial Museum is another worrying one."
The Lace Centre closed on Tuesday after being in the city for nearly 30 years.
Historians accepted the building would be challenging to maintain for a new tenant but said it should not be overlooked because of the economic situation.
Richard Granger, chairman at The Lace Centre, said: "I would hope that the building is put to good use."
He said it was a shame the centre had had to close and added the closure of the nearby costume museum had contributed to the fall in visitor numbers.
Conservationists have called for the council-owned building to be used as an information centre to attract tourists and inform about Nottingham's history.
The council said it had no immediate plans for the building but that it welcomed ideas from the public.