The National Trust has put its insurance affinity business out to tender at the end of a five-year contract with Norwich Union (NU).
NU is one of a number of insurers and brokers asked to tender for the home and motor account, thought to be worth £4m GWP.
A National Trust spokeswoman said: "We expect to receive the tenders next week and will be looking though them over the next couple of months.
"We expect to make a decision by December when the current agreement with NU runs out, but [NU] may indeed be successful."
NU currently offers members of the National Trust a 10% discount as well as donating 10% of all premiums to the charity.
The insurer estimates that one listed building per week is damaged or destroyed by fire, many of which are preventable.
Other risks include exposed timber floor structures, walls lined with combustible materials, thatched roofs and hidden voids in floors, walls and open roofs, it said.