Part of the Winter Gardens is set to be demolished to improve access for workers bringing stage equipment to the venue.
But the area is not considered part of the historic fabric of the Grade II listed building.
A planning application has been submitted seeking permission to demolish the top deck of the two-storey private car park and the former furniture shop, which both front on to Leopold Grove.
If permission is granted, work is likely to start in the new year and be completed in time for next Easter.
A ground floor car park would be retained, with the number of spaces reduced from the current 107 to 64.
Michael Williams, managing director of the Winter Gardens, said: “The car park is in a poor state of repair. It was only ever put up as a temporary building we believe, many years ago.
“The demolition will improve access to the Opera House for large vehicles bringing in stage props for the shows, so it will be a real positive for the venue.”
Elaine Smith, of the Winter Gardens Trust, said she welcomed the move.
She said: “Many people don’t even know there is a car park there, but it is a bit of an eyesore now and there is no historical merit in that part of the Winter Gardens.
“As we hopefully attract more and more shows like Mamma Mia! to the Opera House, we will need better access for more large vehicles bringing in stage scenery etc.”
Provided planning permission is granted, the scheme will be put out to tender, funded by the Winter Gardens. No date has yet been set to decide the application.
Listed building consent also required for work
The car park dates from the 1930s and is an early example of a multi-storey car park.
The furniture shop was built in the 1960s but is not included in the area of the venue protected by the listed building status.
As well as planning permission, an application has also been made for listed building consent.
The shop premises formerly housed a soft furnishings store which closed a few years ago.
Since then, that part of the building has also been used for car parking.
The car park is only for the use of workers at the Winter Gardens and is not been open to the general public.