Radio presenter John Humphrys has urged the BBC to consider axing its digital TV channels rather than cut funding for its core radio and TV programmes.
John Humphrys joined the BBC in 1966
Humphrys, 64, told the Independent he was "massively concerned" at the prospect of further cuts at Radio 4's flagship Today programme.
He fears Today, which he has presented for 20 years, could have its funding cut by as much as a fifth.
In a statement the BBC said it was "committed" to providing quality.
The corporation faces budget cuts in several areas after the government imposed a lower than expected licence fee settlement earlier this year.
Humphrys told the newspaper: "We have already cut our budget by about 15% in the last few years and there are rumours - I've no idea if they are true - that we might have to cut as much as another 20%. We are then left with virtually no reporters.
He added: "If continuing with channels like BBC Three and BBC Four, if funding those channels means the price to pay is that there must be damaging cuts to core programmes then I don't believe it is a price worth paying.
"The case cannot be made if the price to be paid is the kind of salami slicing which meant Today not just suffers but is seriously damaged."
Humphrys' comments follow similar calls made by BBC Panorama journalist John Sweeney at the recent Edinburgh TV festival.
He said the BBC should "shoot a white elephant or two" instead of taking money away from current affairs, adding it would be "better" to close BBC Three or BBC Four.
Newsnight presenter Jeremy Paxman also described the licence fee as "an idea of the 1950s", warning that it would be hard for his programme to survive in its current form if further cuts were implemented.
In a statement, the BBC said: "The BBC must ensure that we meet our six public purposes, as set out in our charter, to deliver maximum public value.
"The licence fee settlement faces us with difficult decisions about how to meet those requirements in the best interests of licence fee payers.
"In the current reprioritisation of budgets, our priority is to deliver distinctive, quality programming and content, particularly in the areas for which the BBC is renowned.
"The reprioritisation may mean the BBC gets smaller and makes less, but we are committed to ensure that will not be at the expense of quality."