Hundreds of thousands of pounds will need to be spent to keep the crumbling Market Hall multi-storey car park open over the next five years.
A council report says it will cost £750,000 to complete the repairs to keep the 588-space Alfred Street car park open until 2021.
Yet Kirklees Council officials have refused to rule out demolishing the 45-year-old structure and starting again.
The documents say a crucial insurance and maintenance policy for the car park expires in just three years and is unlikely to be renewed.
The admission raises questions for the long-term future of the car park – the second most popular in town and the most important for the council.
The car park report has been written for senior councillors in the cabinet this week.
It recommends proposals for beyond April 2019 are considered.
But the council denied any immediate action was being taken.
A spokesperson said: “No decision has been made on the future of the Market Hall Multi Storey Car Park after 2019.
“The council will need to consider all the information available before making a decision and this is not expected to take place in the near future.“
The top two floors of the concrete car park were closed off for several weeks in 2015 to complete essential repairs.
Twice-yearly inspections of the state of the ageing building continue.
Council Highways officials say only the Kingsgate shopping centre car park is more popular with motorists.
But Alfred Street is the biggest money maker for the council and the most convenient for Kirklees’ own Huddersfield Town Hall.
Councillors have been warned that failure to maintain the state of the car park could lead to parts of it being shut again, costing the authority vital income.
Parking payment methods are changed in the car park in May 2014, when it reverted back to a pay and display system.
The car park had operated a Pay on Foot system since 2006.Pay on Foot requires motorists to take a ticket at the barrier on entering the car park and then pay at the end of their visit. From May that year, the car park will once again become pay and display.