Former BBC director-general Greg Dyke said he knew nothing of the allegations until two weeks ago.
Speaking on Radio 4's Any Questions, he said: "Jimmy Savile was long gone by the time I got to the BBC, and I hadn't worked there before.
"I look back at who was head of light entertainment in those days, and you come to really quite venerable figures like Bill Cotton and Jim Moir and I cannot believe - these were men of great integrity, I mean Jim Moir was a devout Catholic - I just don't believe they would have condoned this.
"We don't know anybody knew yet and that will be the interesting thing to find out, and that's what the inquiry will find out, who knew. Of course the problem is there's hardly anybody left at the BBC who was there at that time."
Several of Sir Jimmy Savile's alleged victims are considering taking legal action against the DoH and the BBC, a lawyer has told ITV News.
BBC director-general George Entwistle offered a "profound and heartfelt apology" to the alleged victims of Sir Jimmy Savile's sexual abuse.
BBC chief tells ITV News UK Editor Lucy Manning he is satisfied with how the broadcaster reacted to the allegations against Jimmy Savile.