O'Neill reacted angrily last week when news of Liverpool's £10million bid for the England midfielder was made public.
Benitez claimed on Thursday he was surprised by O'Neill's indignation because the pair had discussed the "idea" of a Barry transfer - which could include a player exchange - "20 days ago".
O'Neill responded on Friday by telling his club's official website: "What idea did I have? I've got absolutely no idea! I have no idea what he's talking about. It's absolutely crazy.
"This is not something I initiated and I certainly was not on the phone to him to ask him about his players either, which I think is something he's trying to refer to.
"That is not true. He mentioned players himself but I might not be interested in any of his players."
He also revealed how unimpressed with the package he was by adding that Liverpool were not offering straight cash but "an offer involving a mish-mash of nameless player exchanges".
Benitez had claimed O'Neill had known "everything about my idea and I knew about his idea".
But O'Neill has rubbished suggestions that Benitez's remarks somehow expose their previous conversation.
He added: "I'm absolutely astonished at this story, 'Rafa Exposes O'Neill'.
"I've never denied speaking to Rafa Benitez so how can you be exposed for something you haven't denied?
"I think Rafa is being very clever here. He gives the impression that there's been constant dialogue. That's simply and utterly untrue.
"He made a phone call to me - I did not initiate the phone call. He asked about Gareth Barry and I said: 'Well he's got a testimonial and two years left to run and he's our best player.' So what would the reaction be?
"I said that I would speak to our owner - obviously because he has a big, big say in the proceedings - and I assumed he would have the same answer as myself - that Gareth wasn't for sale.
"So I'm astonished to read this. The next conversation I had with Rafa Benitez was last Friday morning when Liverpool had put in a faxed offer to us which we received on Thursday afternoon."
