The Heritage Lottery Fund (HLF), which gives out around £300m a year, is considering widening the range of applicants to which it gives grants. New recipients could include cemeteries and privately-owned sites.
At present, the body's rules of governance prevent it from giving grants to organisations such as privately-owned stately homes or historic grounds. However, a new discussion process is currently underway that could pave the way for major change.
The consultation, which will end on 26 April, has invited views from anyone interested in the work of the HLF. At a symposium held in London, head of operations Robert Bewley said: "We currently don't fund any project for private benefit. But we may have to do more to support heritage in private ownership."
He suggested that private sites such as stately homes might be able to get grants if they were able to provide public access - at least for certain periods - free of charge. "We will have to prove that there is a public benefit," he said.
He added that the Parks for People initiative, which awards grants of between £250,000 and £5m, could extend its remit to include cemeteries.
"There are cemeteries that are used for public recreation and quiet enjoyment. We feel that these should be eligible for HLF funds."
He said he would be "surprised" if these measures were not put into effect as a consequence of the ongoing consultation.
In addition, the HLF hopes to simplify its procedure for giving out small grants - between £3,000 and £200,000.
The grant-making body also plans to assist councils struggling to meet management requirements for projects it has funded. It hopes this will help protect front-line services.
An HLF representative said: "If a park is worried that it may breach our contract then it should tell us at the earliest opportunity so we can work together on finding a good solution."
£527m - Value of grants distributed among 550 public parks across the country by the Heritage Lottery Fund since it was established.