Plans submitted to the council propose turning offices at The Mall into 14 new homes.
Six flats would be created on the first floor of the building, with a further eight on the second floor.
The application asks for confirmation that the change of use falls under permitted development, which would mean that planning permission for the new flats is not needed.
Planning documents state that the scheme would not involve any external alterations, or changes to the mass and scale of the shopping centre.
The applicant says: “The proposed conversion is not expected to generate significant additional traffic and will not impact transport infrastructure more than the existing commercial use.
“The site is located in a relatively quiet area, resulting in limited noise impact from existing commercial and adjoining premises, in particular outside the office hours.”
They add that the building already has double-glazing, providing good sound insultation but that they would be willing to fit new windows if further measures are required by the council to mitigate noise.
The application was submitted last month and is still awaiting a decision from council planning officers.