Jonathan Powell said the former British Prime Minister was convinced he could use talks to persuade the group's Army Council to give up their weapons.
'Tony was always convinced of the powers of persuasion that he had to win people over,' Mr Powell told The Guardian, which is serialising his book about the peace process.
'About three or four times he suggested to Gerry Adams that he should meet the IRA Army Council. Adams said 'well I'm not really sure about that'.
'One time he said 'yes, maybe', but then it came to nothing,' said Mr Powell, adding that the IRA men 'could have worn masks' to conceal their identities.
Mr Powell (below), who was one of the former Mr Blair's key advisers throughout his ten years in Downing Street, was a key player in securing the Good Friday Agreement.
He defended the decision to concentrate on dealings with Sinn Féin and to offer concessions.
'We certainly believed there was every chance that the IRA might go back to violence, just as they had with the Canary Wharf bomb (in 1996),' he said.
The revelation of the proposed meetings with the IRA came as Mr Powell said the Ulster experience suggested the British government should also talk to al-Qaeda.
