They hope the agency could entirely replace the IMF in bailout scenarios, helping out struggling eurozone countries who need to borrow money.
Among its enthusiastic backers is French President Emmanuel macron who is pushing for a tighter EU.
But, according to Politico, the nations do not want MEPs and Eurocrats to have a say because they don’t trust them to make cool-headed decisions without getting weighed down in politics.
“It wouldn’t be able to handle the ‘too-big-to-fail’ countries.
“That’s why it’s better to keep intergovernmental control.”
The move has caused uproar in Brussels, with MEPs accusing the council of a power grab.
They say elected representatives will be ignored and effectively blocked from holding the agency to account.
Leader of the Socialists and Democrats group, MEP Udo Bullmann, told Politico: “If member states intend to continue down this path they are committing a grave mistake.
“Our group is adamant that further integration in economic and fiscal policy must occur within the Union framework, based on the community method with full parliamentary involvement.
“This is what we will keep fighting for.”
Council officials want to use an existing task force to create the new agency.
If successful, it would completely avoid being held to account in the European Parliament.
The controversy is expected to be discussed when European leaders meet at their summit next month.
French President Emmanuel Macron is a leading supporter of the plan, wanting to strengthen ties within the eurozone and make it more resilient to financial shocks.
The ESM has previously acted as a safeguard to member states in financial trouble, providing instant financial assistance.
It was instrumental in quelling the sovereign debt and banking crises that plagued several EU states following the 2008 recession.