The airport is one of four in the Swedish capital and it is a hub for domestic flights, with links to thirteen destinations.
But the parties that make up the city's locally elected coalition government argue that it should shut in just under a decade.
The Social Democrats, Green Party, Left Party and Feminist Initiative released a statement on Wednesday saying:
"In order for Stockholm to continue to grow, the city needs land to create new housing and infrastructure. Bromma airport should be decommissioned".
Jan Björklund, leader of Sweden's Liberal Party, which was part of the previous centre-right national coalition, is among those who has already criticized the plan.
Bromma Airport "connects many regions with the capital and means that businesses can operate in many places in Sweden," he told news agency TT.
He argued that it could lead to 20,000 job cuts.
Niklas Nordström, who is Deputy Mayor of Luleå in northern Sweden agreed:
"I get so frustrated when this becomes a local issue…Bromma is a national interest and essential to all of Sweden so people can have access to and from the capital."
The Social Democrat politician added:
"This creates concerns in other parts of Sweden about our economy that we do not need."
The plan to shut the airport will only go ahead if it is agreed on by Sweden's national parliament.
Prime Minister Stefan Löfven's Social Democrat party has previously said it is against the closure of Bromma Airport.
On Wednesday the party said it was still considering the issue.
National Green Party co-spokesperson and Education Minister Gustav Fridolin said that he agreed with the proposal, adding that the current housing shortage in Stockholm and other large cities was affecting Swedes' job prospects.
"So many young people who find their first job or are moving to Stockholm to study cannot find a place to live, and this really threatens the job market."
Liberal Party leader Jan Björklund told news agency TT that he suspected the proposal would not end up becoming a reality.
"This is an issue that must also be approved by parliament and my spontaneous assessment today is that there is no majority for the closure of Bromma".