Police say there could be more than 200 victims, leading one child-protection charity to say that Savile could rank among Britain's most prolific child-sex predators.
In a sign of how the scandal may spread, the BBC said Tuesday that it was looking into claims of sexual abuse and harassment against nine other current and former employees and contributors.
As increasing numbers of BBC executives come under the microscope over what they knew about Savile - and why the posthumous expose about his sexual crimes was blocked from being broadcast - Thompson is being quizzed about his role as well.
Thompson, 55, was the BBC director-general from 2004 to last month.
In a letter to Conservative lawmaker Rob Wilson, Thompson laid out his defense, saying he never worked with Savile, never worked on any of the entertainer's programs, and indeed, never met the man. Referring to the increasing number of BBC employees who have come forward to say that Savile's interest in young girls was widely rumored, Thompson said he had never been aware of the whispers.
"If I had," he said, "I would have raised them with senior colleagues and contacted the police."
The controversy over Saville was compounded when it emerged that an investigation into his misdeeds by the BBC's own Newsnight program was shelved last year only weeks before the broadcaster aired a glowing holiday tribute show to Savile.
Now, journalists and lawmakers are asking whether BBC bosses canned the Newsnight show to protect their star, a prodigious charity fund-raiser widely eulogized after his death last year at age 84.
With Thompson about to move from one of the most important jobs in the British media to one of most important jobs in American journalism, exactly what he knew - and when he knew it - could be critical to his future career.
Thompson acknowledged being warned by a BBC journalist during a company cocktail party late last year about what was happening at Newsnight, but he said the journalist never "set out what allegations Newsnight was investigating or had been investigating."
Thompson said he followed the matter up with other executives who told him the Newsnight investigation was canceled for journalistic reasons - suggesting there wasn't enough evidence for an expose on Savile.
"I had no reason to believe that anyone in the BBC was withholding controversial or incriminating material," Thompson wrote in his letter to Wilson, the lawmaker.
Wilson said Thompson's fitness to serve as the New York Times CEO depends on the outcome of the various inquiries.
A call and an e-mail to the New York Times seeking comment Wednesday were not immediately returned.
