Today co-host Evan Davis says the programme should open up its regular Thought for the Day feature to speakers who are "spiritually minded secularists" rather than always people of faith.
Thought for the Day is the controversial 7:45am spot that many have argued shouldn't have a place at all on the BBC Radio 4 flagship news programme.
Davis said: "I think there's a very serious debate about whether the spot - which I would keep - might give space to what one might call 'serious and spiritually minded secularists'."
"I don't think Thought for the Day has to be only people of the cloth," he told The Independent.
A religious segment has been a consistent part of Today for all of its 55 years on air and, in fact, similar items have run between 7:30 and 8:00am as far back as 1939.
Ten years ago a campaign to get the slot changed resulted in the Today programme commissioning Professor Richard Dawkins to provide an alternative and secular Thought for the Day on 14 August 2002, although ultimately it was aired outside the usual slot. BBC Radio 4's audio of that broadcast is not currently available but you can see a transcript and also read Dawkins's later response to listeners.
BBC Radio 4 is unlikely to drop Thought for the Day entirely but if you could decide, would you keep it to "people of the cloth" or change it to include secularists?