The comedian worked with Savile - who died in 2011 - many years ago on The Sunday Show, before Savile was exposed as a serial sex offender with many victims.
According to the Mirror, Kay opens up about their encounter in his new book Big Adventures On The Small Screen.
The star explained that he wanted Savile to come on the show and that the presenter agreed, in return for £500 in cash and an expensive box of cigars.
"The only hint I got of Jimmy being immoral in any way was when he met our executive producer," wrote the Phoenix Nights and Car Share star.
"I remember she offered him her hand, which Jimmy took, then he flipped it round to kiss the back of it, but before his lips touched her skin I saw a quick flick of his tongue licking the back of her hand. Urgh! What was all that about?"
Kay said that he and the producer talked about it later and that she said to him: "He licked the back of my hand."
"I know, I saw him, the dirty old perv," he replied.
Savile died in 2011 at the age of 84 and then the following year his crimes were exposed.
It was discovered that he had used his celebrity as well as his involvement in charities, hospitals and prisons to abuse hundreds of people over the years.
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