Smith, who died in 2010 aged 82, reportedly bonded with Savile after meeting him at a medieval banquet forty years ago.
In his autobiography Big Cyril, the MP whom police have now acknowledged abused young boys, recounts meeting the DJ.
He said: "I once attended a medieval banquet at Worsley, Lancashire, along with Jimmy Savile. When I joined in the community singing, Jimmy blurted out: 'You've got a nice voice there, Cyril, you must come on my programme!' That's how I ended up singing 'She's a Lassie from Lancashire' on Clunk Click."
This week Greater Manchester Police (GMP) admitted there was "overwhelming" evidence the 28-stone MP sexually and physically abused young boys in the 1960s.
The former MP for Rochdale was elected to parliament in 1972 and was dogged by rumours of abuse throughout his career, although charges were never brought.
According to GMP, which has now assumed full responsibility for the case, prosecutors were given evidence about Smith three times - in 1970, February 1998 and March 1999 - and each time missed their chance.
Police are investigation allegations Savile abused children throughout his career as a DJ and TV personality.
Police are following 400 lines of inquiry as part of the investigation into Savile's activities, and the BBC has launched an inquiry into the culture and practices at the broadcaster during the era of the alleged abuse.