The inquiry by former judge Janet Smith found Savile's behaviour had been recognised by executives at the world's biggest public broadcaster but they took no action to stop him, according to the Observer newspaper.
A police investigation concluded last year that the television and radio presenter, who died in 2011 aged 84, was a predatory sex offender who abused children as young as eight over more than 50 years.
It identified 450 victims but the Smith inquiry suggests up to 1,000 people were abused by Savile while he was working for the BBC, according to the Observer.
Peter Saunders, chief executive of the National Association for People Abused in Childhood, which has been consulted by Smith's inquiry, said many people at the BBC admitted knowing about Savile's behaviour.
"The other thing I have found extraordinary, and very sad, is the number of people I have spoken to connected to the BBC -- and that is a lot of people -- who said: 'Oh yes, we all knew about him.'," Saunders told the newspaper.
The Smith inquiry, which is expected to report next month, is likely to throw the publicly-funded BBC into fresh turmoil.
The Savile revelations sparked a crisis at the corporation over how he was able to carry out such attacks and about the BBC's failure to report the claims against him when they were first raised in the weeks after his death.
Director-general George Entwistle resigned in the wake of the scandal, and was replaced by Tony Hall.
Savile was one of the biggest TV stars in Britain in the 1970s and 1980s, and used his fame as a presenter of the BBC chart show "Top of the Pops" and children's programme "Jim'll Fix It" to rape and assault his victims.
But the BBC is not the only organisation with questions to answer.
The health ministry is currently investigating alleged abuse of patients at state-run hospitals, while a police report last year found that officers had failed to follow up evidence against Savile dating back as far as 1964.
The publicity over Savile prompted a number of women to complain of abuse by other television stars from the same era, a number of whom are now facing criminal charges.