Rossi reveals the sleazy offer came in the late 1960s when the band made its first appearance on U.K. music show Top of the Pops, which was presented by Savile.
Prior to a performance of their debut single Pictures of Matchstick Men, Rossi alleges the late presenter - who is currently at the centre of a huge child sex scandal in Britain - tried to lure him to a dressing room full of "tarts".
Rossi tells British newspaper the Daily Mirror, "The first time ever at Top of the Pops something went on. Our dressing room was away from his. But he said: 'Come here later on because there's going to be something. Come and see me tarts, some f**king tarts we have got in.'
"I was 18 but I just said 'Get out of it'. I wasn't long married at the time. It didn't enter my mind at all."
Cops in the U.K. have launched a criminal inquiry into reports Savile molested up to 300 youngsters throughout his long-running career at the Bbc before his death last year (11).
Rossi has now spoken out to brand the Tv presenter "odd", and insists a fellow 1970s star - Wizzard frontman Roy Wood - also had suspicions about Savile.
The Whatever You Want hitmaker adds, "I remember hearing stuff but I never saw anything. But everybody found him very odd. Parents would drop their daughters at Top of the Pops - it was a completely different world back then.
"I keep hearing 'How did he cover it up for so long?' I heard he paid a lot of people off. But where did he get the money? I think there is a lot to come out about it.
"Even Roy Wood texted me the other day and said 'About time they got that b**tard.' Yep. Everybody heard stuff about him but never saw anything."