Sir Roger, also a former BBC governor of Wales, told BBC News that he heard rumours about Savile from London-based Children in Need staff.
He said that he would have stepped down as Children in Need UK chairman if Savile had become involved in the BBC's corporate charity.
Police now believe that Savile, who died last year, may have abused as many as 300 people over a 40-year period. There have been allegations that he had often specifically targeted vulnerable young people for the sexual abuse.
"I think we all recognised he was a pretty creepy sort of character," Sir Roger said.
"When I was with Children in Need we took the decision that we didn't want him anywhere near the charity and we just stepped up our child protection policies which again would have put him at risk if he tried anything.
"So the way that we dealt with it was by stepping up our child protection policies."
Sir Roger's comments come as the BBC starts a major review of its child protection policies to see if they are still 'fit for purpose' following a string of shocking revelations about Savile, who appeared on BBC radio and TV in the 1970s and '80s.
Sir Roger said that Children in Need was always on "red alert" against potential paedophiles getting involved with the charity group.
> Jimmy Savile: Ex-ITV newsreader 'laughed at' after raising concerns
> Jimmy Savile's relatives 'unaware of his darker side'
"We knew that the biggest thing to guard against was the paedophiles," he said.
"They were just like flies around the honey pot. Not just in the fundraising but also in the distribution of funds.
"I mean if we had given money to a paedophile group, the sky would have fallen in on the BBC. So we were very, very careful, we were on red alert."
But even though he had concerns about Savile more than a decade ago, Sir Roger said that he was unable to take the matter further without evidence.
"If you're going to go on the attack and make claims against him then you'd need evidence, hard evidence that simply wasn't there," he said.
"But if you're protecting yourself you can do that without evidence."
He added: "We did everything we possibly could to protect the kids. That was what I felt to be important, that was my responsibility."
Children in Need said that it was investigating the comments made by Sir Roger.
A BBC Trust spokesperson added: "The Trust shares the horror felt by the wider public about the appalling allegations of child abuse at the BBC and we are determined to get to the bottom of what happened."
Photo gallery - Sir Jimmy Savile:
Copyright: flickr/BBC Pictures