Cameron said that the claims from a number of women which have emerged over recent weeks that they were abused by Savile as teenagers were "truly shocking".
Five women alleged that Savile sexually assaulted them as teenagers in a documentary aired on Wednesday.
The allegations against Savile should be looked into by the BBC - which employed Savile at the time - and, if necessary, by the police, The Mirror quoted Cameron as saying.
Cameron told BBC1's Andrew Marr Show: "I think it is pretty shocking, the allegations that we are reading. They need to be properly looked at, properly investigated.
"It seems to me it is very important that the organisation, the BBC, does that itself.
"But from what I have read - and that is just as a consumer of the media - truly shocking things have been said."
Last week, the BBC's new director general George Entwistle had urged BBC staff to "come forward" and talk to police if they have any information about alleged sexual abuses by Savile.
Last week, in an email to staff, Entwistle said he was "appalled" by the allegations made in an ITV documentary about the former presenter.
No complaints were received at the time of the alleged abuses, the BBC said.
Meanwhile, the Scotland Yard is leading an "assessment" of the allegations.
"Our priority will be to ensure a proportionate and consistent policing response putting the victims at the heart of our enquiries. It is too early to say how many individual allegations there are, and we will be making contact with all those concerned in due course," a statement from the Metropolitan Police said last week.
Savile, a jocular host of children's shows on British radio and television from the 1960s to the 1980s, died in October last year aged 84.
