Jeremy Paxman has been criticised for attacking the BBC's proposed cuts, which could see 2,800 staff made redundant.
The Newsnight presenter had questioned the wisdom of the budget reduction scheme in his speech at the Edinburgh Television Festival, commenting that the reported 20 per cent decrease in the programme's budget would jeopardise its future.
"It is unsustainable," he said. "I cannot see how the programme can survive in anything like its current form if the cuts are implemented."
However, Sir Michael Lyons, chairman of the BBC Trust, has argued that Paxman and fellow news presenter John Humphrys should not publicly express their dismay at the proposed cuts to the budgets of the news and current affairs departments.
"We live in a country which prides itself on the quality of its debate. However, in most companies you would not have members of staff openly debating strategy and whether it's right or not," Sir Michael said.
"To say it's untidy is perhaps an understatement."
Humphrys, presenter of Radio 4's Today programme, had argued that cancelling digital channels BBC3 and BBC4 - watched by "six men and a dog" - would be a better decision for the corporation.
Sir Michael stressed that the comments made by Paxman and Humphrys were unhelpful in the grand scheme of things.
"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.
BBC director general Mark Thompson is to present his cost-cutting plans to the BBC Trust on Wednesday, with a licence fee shortfall leaving a £2 billion gap in funds.