Members of its planning committee will be asked to approve the new 2,600m2 warehouse at the city's naval base when they meet on Wednesday.
A report published ahead of the meeting says the new building would be an 'important facility' for the Ministry of Defence and that the development meets planning policies aimed at using the land for such a purpose.
Submitted earlier this year, the planning application proposes the construction of a warehouse building on the site of the now-demolished foundry 'to provide a logistics store to support the Queen Elizabeth class carriers'.
According to the plans, it would be built between the four listed chimney stacks linked to the former foundry, which were left standing, next to No 2 Ship Shop.
'It is proposed to build a new QLC Store on the site of the former No 1 Smithery to provide a logistics store to support the Queen Elizabeth classcarriers,' a statement submitted with the application says.
'The building is typically industrial in nature to provide a warehouse-style storage facility. The footprint of the building is kept within the four remaining chimney towers and will not impact physically upon them.'
No objections have been submitted to the and the council's conservation officer said the warehouse was 'appropriate' for its setting and welcomed the decision to keep the proposed building's height below that of the towers.
A decision on the application will be made at next week's planning committee although councillors will be asked to grant planning permission.
'The proposed building would provide important storage facilities for the operation of the naval base and would accord with the Portsmouth Plan,' a report published ahead of the meeting says.
'The design and layout is considered acceptable and would preserve the setting of the adjacent listed building and conservation area.
'Subject to conditions, the development would comply with the relevant localand national policies and is therefore recommended for conditional permission.'
It adds that these conditions, which would require the warehouse is built within three years, would also mitigate any environmental harm the development would cause to the protected Portsmouth Harbour area.
A final decision will be made at Wednesday's meeting.