Thompson was challenged by a columnist in The New York Times, just weeks before he takes over as the new chief executive of the paper.
Respected journalist Joe Nocera was forthright in his criticism of his incoming boss in a column titled 'The Right Man for the Job?' on Tuesday (October 30).
He questioned whether The New York Times owners the Sulzberger family had made the right choice in appointing Thompson, who ended his almost eight-year reign at the BBC this autumn.
Nocera feels certain that there was a "cover-up" involved in the controversial decision to drop a Newsnight investigation into Savile in December last year, when Thompson was still in charge of the BBC.
"Plainly, the answer is yes. What is far less certain is how high the cover-up went," he wrote.
He challenged Thompson over why he did not request more details about the content and tone of the investigation when he was informed about it last year.
"But, again, they did nothing. Thompson winds up appearing wilfully ignorant, and it makes you wonder what kind of an organisation the BBC was when Thompson was running it - and what kind of leader he was. It also makes you wonder what kind of chief executive he'd be at the Times."
Thompson is due to start as chief executive of the New York Times Company on November 12, but Nocera - who has been with the paper since 2005 - said that he has already been getting to know his staff.
Nocera noted that Thompson's tenure at the BBC included an international expansion and strong digital growth, which are "two areas where The Times could use his skills".
However, he went on in his column to question why Thompson did not act on the Savile allegations in February 2012, when several newspapers in the UK reported that the Newsnight investigation had been dropped, claiming it was to save the BBC's reputation.
"Since early October , all anybody has asked about Thompson are those two most damning of questions: what did he know, and when did he know it?" Nocera wrote.
"Although he (Sulzberger) declined to be interviewed for this column, he appears to have accepted Thompson's insistence that he knew nothing about the explosive allegations that became public literally 50 days after he accepted the Times job. Sulzberger is backing his man unreservedly," Nocera wrote.
"For the sake of Times employees - not to mention the readers who want to see a vibrant New York Times Company - let's hope his faith in Thompson is warranted. Otherwise, the BBC won't be the only organisation being asked tough questions about its judgment."
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