Nolan shared the news about the late sex predator's troubling invitation with her shocked Loose Women co-stars Jane Moore, Denise Welch and Katie Piper live on the ITV show.
The now 57-year-old chat show panelist explained that she and her sisters appeared on Top Of The Pops when she was a teenager, but although she was too young to perform, Savile invited her to stand beside him on stage.
She explained that his invitation to join her in his hotel room after made her subsequently not want to appear on the show if he was hosting it as she found him "creepy".
She said: "I was 14 and my sisters were appearing on Top of the Pops and I was too young at that stage.
"He asked could I stand on the podium with him to introduce them and then, once they'd done their bit, he said to me: 'Where do you live now?' And I said I was still in Blackpool to which he said: 'I'm there next week and I've got a suite at a hotel, you should come and visit me.
"But nothing happened, I didn't go and I thought he was a creep. But he was one of them. We'd meet him and he'd take your hand to kiss your hand and he'd lick your hand."
She added: "It's difficult for me to talk about that scenario as I had with him, as it's nothing compared to what he did to those victims."
Nolan, who at he height of Savile's fame, was topping the charts as the youngest member of family band The Nolans, also added that she was not surprised that his abuse came to light after his 2011 death.
For decades Savile was beloved in the UK and considered a national treasure, thanks to unique and personable presenting style as host of top-rated BBC shows such as Top of the Pops and Jim'll Fix It.
He also endeared himself to the nation for his endless campaigning for various charities.
He was also a friend of Prince Charles and the late Prime Minister Margaret Thatcher famously rallied for him to receive a knighthood.
Following his death, however, hundreds of allegations of his abuse of minors, including vulnerable children in hospitals, over a time period that spanned five decades were made public.
The late star is now the subject of two part Netflix documentary A British Horror Story, which following its release last week, has become the streamer's most watched show in the UK.
Watch: Documentary shows Jimmy Savile dodging probing questions