Shropshire Council plans to carry out replacement and repair work to Rowley's House and Mansion – the Grade II* listed timber buildings off Shrewsbury's Barker Street in the town centre.
Dating back to the 1500s the buildings have in recent times been surrounded by scaffolding to protect parts which need repair work.
The council application asks for listed building consent to replace and repair panels, as well as some parts of the timber frame of the building.
Planning officers are recommending the proposal is approved – and the authority's North Planning Committee will take a final decision at the meeting on Tuesday.
Shrewsbury Civic Society has welcomed the move – and the potential for the scaffolding surrounding the building to be removed.
In a statement submitted in response to the application the civic society said: "Shrewsbury Civic Society is pleased to see progress being made on the restoration and repair of one of Shrewsbury's most iconic buildings.
"We are also pleased to note that it is the intention to remove at least two of the scaffolding towers as soon as possible."
Historic England, which was also consulted on the application, said the building had major historic importance.
Built in the late 1500s by Roger Rowley, a successful wool merchant, the timber framed Rowley's House, and brick Mansion built by his son in 1618 are located within the core of the Shrewsbury Conservation Area.
The interconnected former houses are Grade II* listed in recognition of their considerable historic, and architectural significance.
The mansion is also believed to be the earliest brick building in Shrewsbury.
A report from planning officer Karen Rolfe said that the work planned would allow the wooden frame of the building to be inspected – and for potential repairs to take place before panels are inserted.
She said: "The proposal would allow for localised timber frame repairs as well as removal and replacement of 20th Century blockwork infill panelling where these would be replaced with lightweight insulated panels comprised of vapour permeable materials.
"With the removal of the existing blockwork panels the timber frame will be inspected with appropriate repair work undertaken prior to the new lightweight panels being inserted."