County Hall officials say they have serious concerns about plans drawn up by campaigners looking to take over Snibston Discovery Park.
The Tory-led Leicestershire County Council wants to downsize the Coalville attraction to a mining heritage museum saving £240,000 from its annual £740,000 cost.
However the Friends of Snibston (FoS) group has put forward an alternative proposal that would see the museum remain as it is but run independently by a charitable trust.
Council officials have been picking over the ideas and have said they are not yet convinced FoS will be able to run Snibston.
A report, to be considered by the council's cabinet next week, says said there are deficiencies in the information provided by FoS which "gives rise to serious concerns."
It says the group has apparently not yet registered with the Charities Commission and that there are significant inaccuracies in its financial assumptions.
The report says: "As matters stand there are grounds for the (council's) cabinet concluding FoS are not capable of providing the service."
The council has told FoS it has until Christmas Eve to provide further information addressing the concerns raised.
Cabinet member for museums councillor Richard Blunt, said: "We can't continue to subsidise Snibston at the current level - which is due to rise to £900,000 per year if we do nothing.
"I said we'd consider the Friends' proposals, alongside our idea of a smaller mining museum.
"We're being very clear with the Friends, by telling them we need more information and clarification and giving them the time to provide it."
Last January, the county council proposed to save more than £240,000 from Snibston Discovery Museum's annual £800,000 subsidy, as part of its £120 million savings. The museum's exhibition hall also requires £2 million of repairs.
The council proposed to meet the savings by developing a smaller, mining-based museum and demolishing the main hall but following an approach from FoS, it agreed to also consider alternative savings proposals.
The council is also awaiting a report on the FoS proposals from an independent financial expert, who was nominated by the Chartered Institute of Public Finance and Accountancy (CIPFA).
FoS chairman Brian Vollar said: "They are trying to do a bit of a hatchet job on us because they want to press ahead with their original plan.
"We are trying to get over all the hurdles they are putting in front of us.
"We'll try to do that by the deadline they have set. It has been an uphill battle.
"We have had to really push and push them to release the information we needed.
"There are also some flaws in their assumptions in that they think the Friends will be running Snibston when we are looking at setting up an independent charitable trust."
Some campaigners say the council is wedded to the idea of closing large parts of the Snibston site so they can be sold off for redevelopment.
