The site would be in the Broomhills housing development site, to the south of Frogston Road East and between Burdiehouse Road and Broomhills Road.
A consultation into the new primary school has now started.
Two public meetings will be held in January and February.
One will be held at Gilmerton Primary School on 31 January between 18: 30 and 20:30 and another at Gracemount Primary School on 9 February between 18:30 and 20:30.
A major development of 633 homes at Broomhills was given the go-ahead last year.
A proposed catchment area for the new school would lead to changes to the current catchment areas of: Gracemount Primary School, Gilmerton Primary School, Liberton Primary School, Gracemount High School and Liberton High School.
Cammy Day, City of Edinburgh Council's education convener, said: "The significant housing development planned for south east Edinburgh means we will need a new primary school in the area because of expected accommodation pressures.
"The statutory consultation starts today and allows parents and school communities an opportunity to have their say on plans for the new primary school and related catchment changes. I would urge everyone to take part as we want to listen and take on board the views of everyone affected by this proposal."
The consultation will end on Friday 3 March and all comments received will be added into a report to go to the City of Edinburgh Council in June 2017.
A new primary school is being proposed for south east Edinburgh after projections showed plans for new housing in the area would lead to accommodation pressures by 2020.