The European Union's chief negotiator on Brexit, Michel Barnier, could address a joint sitting of the Dáil and Seanad next month.
RTÉ News has learned that politicians are looking at Thursday 11 May as the most likely date for the speech.
A formal invitation must still be forwarded by the Dáil Business Committee to Mr Barnier, but initial contact has been made and the response has been positive.
This could be viewed as a clear indication of the importance of the Brexit negotiations for this country as it would be the first time such an invitation has been extended to a politician overseeing talks.
The honour is usually only reserved for visiting prime ministers and presidents.
Previous addresses to the Oireachtas included major speeches by former US president John F Kennedy in 1963 and Nelson Mandela in 1990, seven months after his release from prison in South Africa.
In December 1995, the then US president Bill Clinton addressed the Oireachtas while three years later the British prime minister of the day, Tony Blair, spoke to TDs and Senators in the aftermath of the Belfast Agreement.
The invitation to Mr Barnier was proposed at the last meeting of the Dáil Business Committee which is chaired by Ceann Comhairle Seán Ó Fearghaíl.