Staffordshire County Council has a 99-year-lease on the Shugborough Estate in Stafford until 2065.
But now it wants the National Trust, which owns the Grade I-listed site, to take it back off its hands.
A spokesman for the National Trust has said it is exploring options for the management of the estate.
Mark Winnington, Staffordshire County Council's cabinet member for economy, environment and transport, said: "We are meeting colleagues at the National Trust to explore the feasibility of relinquishing our lease and passing the management of the Shugborough Estate to them."
The council said it expected to spend Â£650,000 this year maintaining and running the Shugborough Estate.
A spokesman said it took the lease on at a time when the National Trust was not as large. He said there was no threat to the building and the council would continue to manage it if an agreement could not be reached.
National Trust regional director Harry Bowell said: "At this stage the National Trust is working in partnership with Staffordshire County Council to carry out early-stage feasibility studies to explore options for the management of the Shugborough Estate.
"It is important to stress that no decisions have been made at this stage."
Shugborough was one of the manors of the bishops of Lichfield in the Middle Ages. The site was purchased in 1624 by William Anson, a lawyer. The current house dates back to 1694.
The National Trust could take back responsibility for a 17th Century estate to save a council hundreds of thousands of pounds a year.