The proposal would see Arundel Court Infant and Junior Schools between Holbrook Road and Arundel Street knocked down to make way for a new three-storey building.
It is thought the new-build would accomodate 630 pupils, 20 per cent more than its current 525.
The classrooms would be built on the schools’ playing fields allowing lessons to continue as normal in the original building. Once the new school is completed the old one would be torn down and replaced with a playground.
Funding for the development will come from central government as part of the Priority School Building Programme.
Portsmouth City Council’s head of education, Cllr Suzy Horton, said: ‘It is a really positive thing that we are creating much-needed school spaces in Portsmouth and any improvement on the quality of learning is great.
‘This will be paid for with external funding and if we can use any of this money to create a new building for the school then that is great.’
Her colleague Cllr Claire Udy agreed. She said: ‘There aren’t enough school spaces in the city. When I had to choose a school for my son it was so difficult. So if they want to rebuild the school to create more spaces there then who am I to complain?
‘People deserve to go to school near their homes.’
However, residents of neighbouring Chatfield House on Fyning Street have raised several objections against the plans.
Bridget Gregory, of Chatfield House, said: ‘The noise levels of the street will increase severely. Already being next to a main road that is used constantly throughout the day and night, the noise that will be of consequence to previous objection points will only add to an already disquiet area.’
Resident Rebecca Hathaway added: ‘The high nature of the proposed building will rob the residents of Chatfield House of any privacy, overlooking not only living rooms but also bedrooms.
‘The proposed new entrance to the school will also result in the use of the unsuitable Fyning Street by large good vehicles delivering to the school which are wholly unsuited to the nature of the street.’
Councillors will decide whether to approve the plans at a planning committee next Wednesday.