The tapes have caused an uproar in Ireland, with the country's prime minister Enda Kenny saying he understands people's "rage".
Transcripts of the 2008 conversation between the bank's then head of capital markets John Bowe and Peter Fitzgerald, Anglo's former head of retail banking, were published in the Irish Independent newspaper earlier this week.
In them, Bowe appears to state that the bank was deliberately hoodwinking the Irish government into thinking that a €7 billion rescue would save the lender, despite knowing full well that a much larger amount would be needed.
The plan, he said, was to get the initial cheque written so the the government would "have to support their money" by making further payments further down the line.
"If they saw the enormity of it up front, they might decide... they have a choice. You know what I mean? They might say the cost to the taxpayer is too high," he added.
Bowe said: "I categorically deny the allegation that I, at any time, misled the Central Bank or was aware of any strategy to do so."
However, Irish taxpayers who footed the bill and have suffered as a result of the economic turmoil prompted by the bank bailouts are furious about the revelations.
And the government has promised to look into launching a public inquiry into the collapse of Ireland's banking system.
"I understand the rage and the anger of so many people who have been affected by all of this," prime minister Kenny said.