The neglected land next to Cuthbertson Primary was once used as a football pitch but the goalposts have long since rusted away and the overgrown grass is strewn with discarded bottles and cans.
Headteacher Hilda Carrick is hoping to raise £200,000 for the 'Govanhill Play Together' project.
She said: "The ground has been in poor repair since I came to the school seven years ago.
"Teenagers have been getting in at night and drinking and causing damage.
"They leave wine and beer bottles and cans. It's become a drinking den."
Deputy head Kirsteen Kennedy said: "It's not really a suitable surface. It doesn't have drainage. It's muddy, boggy, uneven and overgrown.
"It has reached the end of its life."
The school staff applied for Lottery funding and were unsuccessful, but the groundwork has been laid for a park that would benefit the entire area.
Mrs Carrick said: "We have planning permission, a survey and lots of ideas from pupils.
"It could be a fantastic facility for the whole community.
"The children tell us they don't feel safe in Govanhill Park, and parents often don't let them play there.
"With the Commonwealth Games, we're trying to encourage children to be more active and this could be a real help."
The school consulted the local community during preparation to apply for lottery funding and 80 residents responded to say they supported the park plan.
Local councillor Soryia Siddique, who heads up the city council's children and families policy development committee, also offered her backing during a visit to the school.
She said: "I'm delighted that the campaign to develop a community play space is gathering momentum.
"I am working with Cuthbertson Primary School management to populate the community space.
"The vision is to create a safe place for children to play.
"This will be a positive project, building community cohesion, resilience, health and well being through play."