Portsmouth councillors are set to consider proposals for a four-storey car park on the northern side of the existing north car park, which is reached from Harvey Road.
If approved the structure will provide a total of 541 car parking spaces and six motorcycle spaces, and it will connect to a new 72-bed ward - that was given planning permission in December - by a link bridge at first floor level.
As reported, plans for a new £58m emergency department at QA at the hospital are also in the works – although a planning application has not yet been submitted.
A spokesman for Portsmouth Hospitals University NHS Trust said: 'Our plans to create additional car parking spaces form part of a wider programme of work to develop the Queen Alexandra Hospital site to provide improved facilities for our patients, their families and our colleagues.
'This week, we started preparatory work on a new ward building which will provide additional beds in a modern environment for patients requiring rehabilitation.
'Our plans to build a new car park alongside the new ward will ensure we are providing much needed parking for patients and visitors in the future, helping to ensure our hospital will serve the needs of our local communities for many years to come.'
Currently there are 801 public parking spaces and 1,411 staff car parking spaces across the hospital site.
On completion of the three developments the numbers of parking spacesare set to reduce by 98 - equivalent to an increase of 247 public spaces, and a decrease of 345 staff spaces.
It is planned the reduction in staff parking will be met by use of the hospital's nearby Fort Southwick park and ride that has 992 parking spaces - of which around 450 available spaces are not used on a daily basis.
A decision on the new car park will be made at a virtual planning committee meeting on Tuesday, March 30 that can be viewed live via Portsmouth City Council’s website.