Mrs May is to hold talks with Enda Kenny later this month
Moves are underway to invite the British Prime Minister Theresa May to address the Dáil later this month.
Mrs May is already due to visit Dublin in the next two weeks, to meet Taoiseach Enda Kenny for discussions on Brexit.
But the Dáil Ceann Comhairle - acting on a suggestion from the Green Party - has invited Mrs May to address TDs as well.
Mr Kenny says he will examine whether a visit can be squeezed into the schedule.
"I'm going to act on the letter received from the Ceann Comhairle to see whether that might be possible or not.
"All I know is that when the prime minister agreed to come here obviously a time schedule was set in place - and I don't have the details of her day other than the indication of coming here to discuss these matters".
Green Party leader Eamon Ryan said earlier: "It is vitally important that Prime Minister May sets out her views on how Brexit will affect this island, following on from her comments in relation to the Common Travel Area and the Customs Union today.
"We are calling on the Taoiseach to extend an invitation to Ms May to address the Houses of the Oireachtas, following on from First Minister of Scotland Nicola Sturgeon’s address to the Seanad on her recent visit."
The proposal comes after Mrs May's address on Brexit in London earlier.
In a speech outlining her government's plans, she said both British Houses of Parliament will vote on the final deal.
She also said the plans "cannot mean membership of the single market".
"Being out of the EU but a member of the single market would mean complying with the EU's rules and regulations that implement those freedoms, without having a vote on what those rules and regulations are."
She also suggested that maintaining that Common Travel Area between Ireland and the UK is "an important priority" in the talks ahead.
While Irish MEPs met in Strasbourg with the European Union's chief Brexit negotiator, Michel Barnier, following the speech.