Model and actress Kelly, 34, is currently promoting her tell-all life story - available 11 September - which includes references to her past relationship with rugby player Danny.
And speaking on today's BBC Radio 1, Kelly suggested that Danny hasn't been happy with what he's read so far.
When asked if anyone had been angry at the book, she told Nick Grimshaw: "Not really, to be honest. They knew I was doing a book and they said, 'Can you send it to us before it comes out?' and I said, 'Yeah, yeah, yeah' and then I just forgot.
"Danny Cipriani is blowing up my phone now saying, 'I'm going to sue you!' I'll soon find out, won't I? Usually they take out injunctions don't they? I thought, 'If I send it to you, you'd probably do that.'"
She then said: "I'd rather get my voice ut there and then go to jail!"
Danny has so far not responded to Kelly's claim.
Kelly went on to say that writing the book had been a "cathartic" exercise for her, particularly as she was writing about events that had happened in the past.
"I'm happy because I have distance from a lot that happened so I can be fair and honest. I don't feel I have bitterness or anger. I'm in a really happy place in my life. I'm in a nice relationship, I'm working in America, I'm doing good things. It wasn't to dig the knife in on anyone. It was nice to put my point of view across and my perspective on things."
Kelly is gearing up to return to LA where she'll be filming NBC sitcom One Big Happy alongside actor Nick Zano and 24 actress Elisha Cuthbert.
NBC announced in May that it had ordered her sitcom pilot to series. It's about a lesbian woman and straight man who are best friends and decide to have a baby together. Then the man meets a British woman, played by Kelly, and things get complicated.
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