The small screen veteran, who died last year (11), has been accused of sexually abusing children during his heyday, and there is growing calls in the U.K. for an official investigation into the claims.
Nolan, who sang with her sisters as part of The Nolans, has now spoken out about her experience of Savile, and reveals he asked her to join him in his hotel suite when she was 14 years old.
She tells Britain's Daily Star Sunday, "I did think 'Oh my God'. It was kind of impressive that this famous Dj had asked me to go with him to his hotel room.
"When someone that famous wants to spend time with you, you're thrilled. I thought 'Oh wow'. But my sisters told me 'That's not right Coleen, that's just weird'.
"Considering what's come out, I feel thankful nothing like that happened to me. If I had gone ahead with it and innocently met him then obviously I would have had the same fate.
"Why else would a fully-grown man ask a 14-year-old girl to go to his hotel room? I had a lucky escape, absolutely."
Her sister Linda adds, "If we hadn't been there God knows what would have happened. It could have gone very wrong. Coleen probably didn't think for a minute what could have happened. It was exciting for her to meet a big TV star. When she told us about the hotel suite she said it would be great and we said 'I don't think so'."
Savile was the focus of a controversial expose titled Exposure: The Other Side Of Jimmy Savile, which aired on U.K. network Itv on Wednesday (03Oct12).