Up to 13 new one-bedroom flats and a three-bedroom house could be built on a section of vacant land.
The new homes are earmarked for Dallas Street near the town centre by Birches Building Company Ltd.
The site once housed commercial properties but were dilapidated and would have needed ‘significant investment’ to bring back into use.
They have since been pulled down.
A total of 16 parking spaces have also been included in the plans, along with a communal garden.
The height of the proposed building will be ‘slightly higher’ than the existing homes on Dallas Street.
The site is already subject to a planning application for five town houses that was granted in 2012.