Ground-breaking talks between the Catholic primate and the Rev Ian Paisley will take place before the end of this month if Dr Seán Brady's officials and the DUP can find a suitable date.
Dr Paisley said yesterday he was willing to meet the archbishop, while Catholic sources revealed that moves involving senior DUP figures to organise talks were well under way.
Contact between the two sides began last Christmas and it is hoped a date can be found in late September before Dr Brady travels to Rome for three weeks.
Dr Paisley said on RTÉ yesterday: "On the issue he wants to talk about, I'd like to hear from him. Having a secret meeting with the archbishop would get us nowhere. Let's get it above board."
A statement issued on behalf of the archbishop last night claimed Dr Brady had already indicated his willingness to meet Dr Paisley and other political leaders.
Dr Brady said: "I look forward to the prospect of engaging with ministers from all parties in the exercise of the civic, social and educational responsibilities of the Catholic Church in a modern, pluralist democracy.
"Such engagement would be an important signal to the whole community that the normal standards of decency, respect and tolerance associated with a modern democracy have become the new backdrop to a more mature and confident Northern Ireland.
"Such engagement on matters of mutual responsibility in the civic domain does not compromise the sincerely held religious convictions of anyone. Indeed, there are many aspects of public policy and social concern, including the defence of religious liberty and certain fundamental moral values, about which we could all agree."
Dr Brady's spokesman said the archbishop "responded positively in July to a letter from Mr Gregory Campbell (a DUP MP) suggesting dialogue on matters of mutual concern. Representatives of Archbishop Brady have also been in touch with representatives of the DUP to progress a meeting between the Catholic bishops and the DUP on an agreed agenda".
Contact has also been made with Lagan Valley DUP MP Jeffrey Donaldson regarding a meeting between Dr Paisley and Archbishop Brady.
Moves towards a meeting follow calls from the PSNI Chief Constable, Sir Hugh Orde, for politicians to follow words of condemnation of sectarian violence with initiatives to build harmony.
The Bishop of Down and Connor, Dr Patrick Walsh, also appealed to community and political representatives to be seen standing together to combat sectarianism.
The Rev Ian Paisley said yesterday he condemned "across the board" sectarian attacks in Ballymena and elsewhere. But he said nationalist leaders also had a responsibility to condemn attacks on Protestant property.
"You have lost the argument when you take to strife," he said. "That's not democracy, that's anarchy. It must be put down with a very heavy and determined foot."
The 79-year-old DUP leader said a stable political future based on power-sharing was achievable in his lifetime, so long as democratic fundamentals have been met.
He would publicly shake the hand of senior republicans only when the constitutional conditions set by prime minister Tony Blair had been met.