The BBC press office told the AFP on Monday it could not confirm the reports, carried on both the BBC News channel and its rival Sky News television, but an official announcement is expected within hours.
Acting director-general Tim Davie, who took over the top job at the public broadcaster following the dramatic resignation of George Entwistle on Saturday night, is expected to set out his plans to manage the crisis later in the day, Aljazeera reported.
According to the BBC report, Boaden and Mitchell have been asked to give up their responsibilities pending an inquiry into why an investigation by the Newsnight program into claims of sex abuse by Savile was dropped last year.
There have been suggestions, which the BBC has denied, that the Newsnight report was axed because it would have clashed with a planned tribute program to Savile, one of the BBC's biggest stars who died in October 2011.
The inquiry is being led by Nick Pollard, the former head of Sky News.
Allegations that Savile may have abused up to 300 children over four decades, including while working at the BBC, have plunged the broadcaster into crisis.
The BBC's problems were compounded when Newsnight, one of its flagship current affairs programs, was forced to admit on Friday that a report the previous week implicating a senior political figure in child sex abuse was wrong.
Entwistle resigned on Saturday after just 54 days as director-general, saying he took responsibility for the Newsnight report even though he had not seen it.
The state funded broadcaster confirmed on Sunday that Entwistle would get a payoff of $715,000.
It said the settlement took into consideration that Entwistle would continue working on BBC business, including two inquiries in the child abuse scandal.
John Whittingdale, the chairman of the House of Commons committee on culture, media and sport, says he was surprised by the settlement and has sought an explanation.