The revelation came as police admitted Savile's sex abuse could have spanned six decades and about 60 victims.
Derek Chinnery, who held the post of Radio 1 controller from 1978 to 1985, told the presenter he wanted to know the truth about "rumours" he had heard.
However, Savile, who died last year, shrugged them off as "nonsense".
Savile worked at Radio 1 from 1969 to 1989 presenting a show of chart songs from previous decades.
Speaking about his acceptance of Savile's denial, Mr Chinnery said: "There was no reason to disbelieve (Savile).
"It's easy now to say 'how could you just believe him just like that?'
"He was the sort of man that attracted rumours, after all, because he was single, he was always on the move, he was always going around the country."
The admission came as Scotland Yard said the sex abuse allegations against Savile, who also presented Jim'll Fix It and Top of the Pops, spanned from 1959 to as late as 2006.
It is pursuing 340 lines of inquiry and so far 12 allegations of sexual offences have been officially recorded, but this number is increasing.
Metropolitan Police detectives are in contact with 14 other forces, including Tayside, as the number of allegations against the former DJ continues to rise.
The BBC has come under fire after it emerged Newsnight abandoned an investigation into the alleged abuse.
The organisation has also been criticised after claims were made that staff were aware of the presenter's behaviour and failed to take action.
On Friday, BBC director-general George Entwistle offered a "profound and heartfelt apology" to the alleged victims as he announced that two inquiries would be launched.
One will look into whether there were any failings over the handling of the abandoned Newsnight piece.
A second independent inquiry will look into the "culture and practices of the BBC during the years Jimmy Savile worked here", Mr Entwistle said.
Sir Michael Lyons, who was chairman of the BBC Trust from 2007 to 2011, welcomed the investigations into Savile's behaviour but added that there was "a degree of hysteria" when controversies arose involving the BBC.
He said: "It clearly has consequences for the BBC, but frankly I think the consequences spread well beyond the BBC.
"There may well be lessons here to learn about the way that we tolerate the behaviour of predatory men, particularly when they are in powerful positions.
"And there may be lessons to learn – I am sure there are – about the license that we sometimes allow to celebrities.
"This goes well beyond the BBC, although there are issues for the BBC to address."
Talking generally about controversial issues at the BBC, he added: "As they emerge the BBC perhaps understandably becomes a very intense focus for people's concern and anxieties.
"After all, it is the national broadcaster, we do want to trust it, we do need to be able to trust what it says, so it is naturally the focus where these cases relate to it.
"But equally you have to say actually there is a degree of hysteria in the extent to which it's focused exclusively on the BBC rather than being seen as something of much wider consequence."
He continued: "What we hear are not just allegations relating to the BBC – although I don't want to diminish those – but also allegations made about hospital and prison contexts.
"If they are proved right here we have a serial offender potentially across a wide range of settings.
"None of that detracts from the importance of the BBC making sure that it understands what happened and makes sure there is no risk at all of such events happening now."