Tettenhall Towers, which sits inside the grounds of Tettenhall College, was once the residence of Wolverhampton's first mayor, Benjamin Thorneycroft.
Under new plans the roof of the Grade II* listed building is to undergo a series of repairs in a bid to preserve it for future generations.
The plans, which have been submitted to Wolverhampton Council, say the work is required to "protect the building integrity for the longer term".
It will see refurbishment and repair works taking place on the flat roofed structure to the rear of the building. Meanwhile separate work to install a new flat roof structure will help preserve the older parts of the building by diverting rainwater, according to the plans.
A statement accompanying the plans says: "These minor alterations to the profile of the roof and parapets will help to protect and prolong the life of the listed building by permitting more robust weatherproofing details and diverting rainwater away from vulnerable internal routings, while offering little or no discernible effect on the heritage character."
The planned work follows a condition report, published in 2014, which described the roof as being in "poor condition" and in need of replacing.
The building, which features a theatre, cellars and a maze of corridors, was built in the late 18th century and has long been considered one of the most unusual in the city.
It was developed into a larger home by Benjamin's son, Colonel Thomas Thorneycroft, a keen inventor.
It has been part of Tettenhall School since 1943 and has hosted ghost hunts.