Both Mr Entwistle and Ms Boaden have not provided responses to the points raised by Panorama.
But news executive Helen Boaden said she "had never heard any dark rumours".
However, neither Ms Boaden or Mr Mitchell were in the decision-making chain that led to Newsnight's broadcast.
Helen Boaden, director of BBC News, said there would be up to 800 post closures in news.
He was "a wry and witty broadcaster of immense experience", according to Helen Boaden, controller of Radio 4.
Ms Boaden, who was head of news when the Jimmy Savile scandal broke, has years of experience in radio.
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Ms Boaden told him that if the Newsnight investigation went ahead, he might have to change the Christmas schedules.
The BBC said once the Pollard Review reports, Ms Boaden and Mr Mitchell "expect to then return to their positions".
Ms Boaden said she "had never heard any dark rumours about Jimmy Savile" but did meet him at a lunch for veteran radio presenters.
Ms Boaden had to step aside for a period from November last year, along with her deputy Steve Mitchell, in the wake of the Savile investigations.
The corporation said it found that neither Ms Boaden nor her deputy Mr Mitchell "had anything at all to do with the failed Newsnight investigation into Lord McAlpine".
Before MacQuarrie's review was completed, BBC News Director Helen Boaden and her deputy, Steve Mitchell, were asked to "surrender all their responsibilities" pending the outcome of the review, the BBC said.
Helen Boaden and Steve Mitchell have been asked to surrender all their responsibilities as head and deputy head of BBC News, pending the results of the Pollard inquiry, I have learned.
The BBC News spokesman confirmed that Mr Thompson had spoken to Ms Boaden "and other directors about the need to have a broad range of presenters on air - including older women".
The BBC's director of news, Helen Boaden, and her deputy, Steve Mitchell, have been asked to "step aside" pending an internal review into the way abuse claims about Jimmy Savile were handled.
My understanding is that Mr Davie believes it is unfair to ask Ms Boaden and Mr Mitchell to continue in their day jobs with the shadow of the Pollard inquiry hanging over them.
An internal email issued by the BBC's director of news Helen Boaden - who returned to her post on Thursday after stepping aside during the Savile crisis - described the recent criticisms of the corporation as "bruising".
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This is in stark contrast to other senior executives at the BBC, including former director general Mark Thompson and director of news Helen Boaden, who both told the inquiry they had never heard any "rumours" about the DJ.
Many said they believed Ms Boaden and Mr Mitchell ought to be put firmly back in charge of news, because of the perception that they would never have permitted the latest child abuse story to have run on Newsnight.
Helen Boaden, who was director of news for eight years, has been made director of radio, while Tim Davie, who has been acting director general for the past four months, moves to a role in charge of the BBC's global activities.
Mr Davie and Lord Patten are understood to believe that Ms Boaden's and Mr Mitchell's decision to withdraw from all decision-making on the way the BBC reports the Jimmy Savile scandal has created confusion at BBC News about who is in charge.
On Monday, the BBC's director of News Helen Boaden and her deputy Stephen Mitchell "stepped aside" from their roles, pending Nick Pollard's report into the management of Newsnight's report into allegations of sexual abuse by the late TV presenter and radio DJ Jimmy Savile, which was dropped.
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The Director of News, Helen Boaden, and the Controller of Radio Four, Mark Damazer, have both made clear that, although Ed will not be presenting Today, they want, and expect, him to remain a part of their plans, on radio in particular, for many years to come.
As for what the Pollard review may conclude about the conduct of Ms Boaden and Mr Mitchell, I understand that Peter Rippon - the suspended editor of Newsnight - does not believe he was put under pressure by either Ms Boaden or Mr Mitchell to pull the Savile investigation.
Panorama found that at an awards luncheon at the Hilton hotel on 2 December 2011, BBC director of news Helen Boaden told Mr Entwistle, the then director of Vision - which oversees BBC TV commissioning and programming - about the Newsnight investigation and its possible impact on the planned tributes to Savile.
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