The former Britain's Got Talent judge moved to Los Angeles in order to start work on Piers Morgan Tonight for CNN in January 2011.
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Morgan revealed that model Kate Moss enjoys kicking him whenever they meet in public.
"She came up to me at some charity thing with Naomi Campbell and gave me a full, haymaking kick," he told The Mirror.
"And then the next time we had dinner in a restaurant, she was opposite me... and kicked me again. She doesn't like me, I don't like her. She kicked me, hard. Right on the shin, repeatedly.
"I looked at her and said, 'Kate, why are you kicking me?' She said, 'Because I want to.' And cackled. She was completely off her head. And I replied, 'Well, can you just stop kicking me, OK?' She looked blank, and gave me another kick. It was a bizarre conversation."
The presenter explained that he has "banned" Madonna from his CNN talkshow, saying: "She's a complete con artist and those arms are just terrifying.
"It's like watching Conan the Barbarian. She's looking even more barbaric than ever at the moment, utterly grotesque.
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"When I got the CNN job I banned her from the show, permanently. She responded by saying she'd never heard of me, but we both know she's lying."
Morgan added that the closest he had come to being "killed" by a celebrity was with Die Hard actor Bruce Willis.
"I once wrote a bitchy piece about his British bride, Emma [Heming], saying she looked like a young version of his ex-wife Demi Moore - proving if you're a superstar you don't have to worry about the normal ageing or relationship process," he said.
"One week later, I was at the next table to them in a restaurant. Bruce stared at me, smirked, and said: 'Embrace death, Piers!' and then started sending me tequila shots until I was nearly drowning - each time with the entreaty, 'Embrace death!'
"Eventually I managed to persuade him to do the same, and the pair of us got absolutely hammered. At the end of the evening, he bear-hugged me, very hard. 'Will I have to embrace death tonight?' I asked him.
"'I haven't decided yet,' he replied. 'Well, if I do, I know how I'll die…' I told him. 'Oh yeah, how?' he slurred.
"'Hard, Bruce. I'll die hard.' And he finally laughed."
Morgan recently described Madonna as a "gruesome drunken aunt" after her Super Bowl performance.
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