Currie Primary, in Curriehill Road, is expected to need up to eight extra classrooms to accommodate more pupils.
One option being looked at by education chiefs is to build on one of the school’s seven-a-side pitches.
Resident Robert Phillips blamed “over-development” of new homes built on the school’s former Curriehill site.
“Here’s another erosion of a perfectly good facility,” said Mr Phillips, 70, whose children went to the school and whose two-year-old grandson attends the nursery.
Tory education spokesman Councillor Callum Laidlaw said “difficult decisions” would need to be made to find classrooms in areas like Currie which are popular with young families.
“That said, as we grapple with childhood obesity and inactivity it is a real shame to lose a football pitch that is not only space used for play but also for PE which is an important part of the curriculum,” he added.
Plans have been submitted to allow the school to build eight extra classrooms on the pitch or the playground.
Another option could be to tweak school catchment areas so some extra pupils attend Dean Park or Nether Currie Primary – leaving Currie needing only four extra teaching rooms.
Council chiefs stressed parents would be consulted on work to be completed for the 2019-20 school year while Currie is assured of retaining its other seven-a-side pitch.
Former Hearts and current Celtic keeper Gordon, 34, attended Currie in the late 80s and early 90s, when it was called Curriehill. Although the school has moved to make way for housing, the sports pitches have remained.
Cllr Laidlaw called for “smarter” ways of tackling knock-on effects of housing developments, including inserting planning conditions for new schools to be built by house builders.
National campaigners Fields in Trust say there are growing fears over the loss of school playing fields and parks to developers. The group recently safeguarded the site where George Best was discovered in Belfast.
Helen Griffiths, the group’s chief executive, said: “Outdoor space plays a crucial role in ensuring the physical and mental well being of pupils in a school setting. Fields in Trust believes that protecting school playing field land should be a priority.
“Whilst not every playing field user aspires to play professional sport, it is the case that every elite sportsperson began their career in a park or playing field.”
City education convener Cllr Ian Perry said: “We are still at an early stage of considering how we tackle the rising rolls predicted for Currie Primary School.
“All options will be considered and there will be more detailed discussion with the both the school community and Sportscotland to ensure there is no detriment to the school’s sporting facilities.”