Red House and Dewsbury museums could close as early as November if senior councillors approve cost-cutting changes to museum and gallery services across the district.
Kirklees Council announced plans to axe the museums, in Gomersal and Crow Nest Park, in July.
It said it faced “severe cutbacks in government funding” and had to make more than £530,000 worth of savings to its museums and galleries budget by next April.
Coun Graham Turner, cabinet member for Creative Kirklees, said: “It is clear that many residents love and value the buildings we have, but if we do not close any of the sites it will be impossible to achieve the savings we need to make.
“With a constantly diminishing budget, we have to change the cultural offer but I believe the proposed changes will ensure that we can deliver a service for the residents of Kirklees that tells our story, in a different and more up to date way.”
The council launched a three week consultation period on the proposals.
Coun Turner said; “Most people wanted to keep all of the museums, but the overall survey responses did not suggest an alternative to the three sites we have identified.”
The Friends of Red House Museum have campaigned against its closure.
Nearly 2,000 people put their name to a petition to keep it open, and the friends group submitted a report which gave 20 reasons why the site should not shut.
Chairwoman Jacqueline Ryder said: “We were always hopeful that the council would recognise the importance of Red House not just in North Kirklees, but for Yorkshire and, with the Brontë connection, internationally as well.”
Dewsbury East councillor Cathy Scott (Lab) also started a campaign for the museum in Crow Nest Park to remain open.
“I have been inundated with people wanting to help to save the museum,” she said. “People were not anticipating this.”
Members of the council’s cabinet will be asked to agree the proposals at a meeting on Monday.
If approved, the council said Red House and Dewsbury Museum would remain open until “at least the end of October”. It would then look to “dispose of” the buildings.
Oakwell Hall and Country Park and Bagshaw Museum would not be affected.
And Tolson Museum and Huddersfield Art Gallery would remain open in the short term until a new Huddersfield Museum and Art Gallery is created.