The Rt Revd John Inge, the Bishop of Worcester, has been speaking as the BBC faces having to plug a £700 million annual cost for providing over-75s with free TV licences, from 2020.
It's been reported celebrities, including Dame Helen Mirren, Lord (Melvyn) Bragg, Sir Terry Wogan and Sir Michael Parkinson could front a campaign being spearheaded by director-general Lord Hall, to encourage voluntary contributions from pensioners.
Bishop John told Premier: "I'd be very worried if that particular provision were to be removed but asking people of their own volition to give it up, I suppose, is something that the BBC is well within its rights to do and maybe it would be a way of people showing their support for the BBC.
"I'd be interested to know what proportion of people would be prepared or want to give up their [free] licence fee.
"I suppose if we think of the BBC as a national institution of great merit then, perhaps, it's something that people would want to support."
The idea is thought to be just one of several options being considered.
A BBC source told the Press Association: "The BBC has asked independent experts to advise on how to go about attracting voluntary contributions from over-75s when the Government reduces its support.
"The Government agreed that the BBC could ask for voluntary payments from those who currently receive free licences as part of the agreement for the corporation taking on the costs of free over-75s licences.
"The work will include analysis and interviewing a range of stakeholders. It will look at options for receiving payments and explore best practice in other organisations.
"The BBC will then look at the best way forward, including whether to run a campaign."
Responding to the latest development, the National Pensioners Convention (NPC) warned a campaign fronted by celebrities could lead to older people being "taken in by this when they should be protected".