Funding of £12m for a Magna Carta exhibition in Lincoln Castle will be lost if the crown court remains there, the county council claims.
The council said the court expressed a desire to move in 2006, so a new exhibition area was planned.
No decision has been made, and funding will be lost if the move is not completed by 2013, the council said.
Her Majesty's Courts Service said it was not currently in a position to vacate the site.
A law court has been in the castle for more than 900 years but the council said the court has outgrown its current location.
The exhibition is planned for the 800th anniversary of the Magna Carta in 2015.
As well as the exhibition area, the council would also like to provide disabled access to the castle walls and an improved education space.
The Heritage Lottery Fund is to provide £8m and a further £4m is to come from the East Midlands Development Agency.
The council has said it will spend £6m on improving the castle.
Councillor Eddie Poll said: "We've been supportive of the court, trying to do everything to relocate them and now they've backed down."
Her Majesty's Courts Service (HMCS) confirmed it had been approached by the county council and asked to vacate the current crown court in Lincoln so the council could create a Magna Carta visitor centre.
A spokesperson said: "HMCS owns the freehold on the site within the walls of Lincoln Castle. Having carefully considered the request, HMCS is not currently in a position to vacate the court.
"We looked at various options for both temporary and long term solutions, all of which were either not feasible in the time or were too costly.
"We have a duty to ensure that we get the best value for every pound of taxpayers' money spent and maintaining the court within the Castle presents the most cost effective option for justice in Lincoln."
The spokesperson added that HMCS would continue to discuss the matter with the council and, if the local authority was able to fund the project, would work with it to find a suitable location for the court.