BBC chairman Sir Michael Lyons has said leading broadcasters should stay out of the public debate on the future of news and current affairs at the corporation.
Humphrys urged the BBC to consider axing its digital channels
He was speaking ahead of the BBC Trust's report into the corporation's six-year plan, which is due next week.
All areas of the BBC are facing budget cuts after the broadcaster did not get the licence fee increase it wanted.
Both Jeremy Paxman and John Humphrys have recently criticised the proposed savings of 3% a year.
"To say it's untidy is probably an understatement," said Sir Michael.
"It's a difficult balance to strike. We live in a country which prides itself on the quality of its debate."
Sir Michael said most companies do not have members of staff and "on occasion... managers" openly debating whether a company strategy was right or not.
He called on them to raise "misgivings and doubts" internally, adding: "I think that the public debate, they are best to stay out of."
"Would I encourage them to make their comments within the internal channels? Yes, I would. Will they all do that? We'll have to wait and see," he added.
Sir Michael warned there would be 'pain involved' for BBC staff
In August, Humphrys, 64, told the Independent he was "massively concerned" at the prospect of further cuts at Radio 4's flagship Today programme.
He said he feared that Today, which he has presented for 20 years, could have its funding cut by as much as a fifth.
Humphrys' comments followed similar calls made by BBC Panorama journalist John Sweeney at the 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 Paxman has also voiced his fears about cut-backs, saying the show could not "survive in anything like its current form" if its budget was slashed by 20%.
Sir Michael's comments came as some of Radio 4's most familiar voices, including Charlotte Green and Peter Donaldson, joined the protest at the proposed cuts.
In a letter, published on The Guardian website, 84 signatories warned of "extremely grave prospects" facing the radio newsroom, with "devastating cuts" that "seriously threaten the quality of the service we provide".
The BBC Trust said it was yet to receive the letter.
It has been reported that up to 2,800 jobs could be lost as director general Mark Thompson attempts to plug the corporation's estimated £2bn budget shortfall.
Mr Thompson will announce the cuts next Thursday, a day after he presents his final plans to the BBC Trust.
Speaking to journalists in London about the six-year plan for the future of the BBC, Sir Michael admitted there would be some "pain involved," but urged staff to "concentrate on the job in hand" and deliver value-for-money to licence fee payers.