The European Union's Chief Negotiator is expected to meet the Taoiseach later.
Michel Barnier is in Dublin to attend the Ireland v France Six Nations game at the Aviva Stadium.
Leo Varadkar will also be attending and both will meet informally at the game.
It follows a week of intense but fruitless negotiations between the UK and EU, and comes ahead of the UK Parliament's vote on the withdrawal agreement on Tuesday.
Meanwhile, DUP deputy leader Nigel Dodds and Steve Baker, the deputy chairman of the pro-Brexit Tory European Research Group, have warned that without concessions from Brussels, defeat in the Commons on Tuesday is “inevitable”.
The warning comes amid reports that Cabinet ministers have told Mrs May the only way she will get her deal through Parliament is if she agrees to stand down by June.
Discussions were continuing in Brussels between officials over the weekend with little sign of a breakthrough.
It follows a Twitter exchange between Michel Barnier and Brexit Secretary Steve Barclay, with Mr Barclay accusing the EU of attempting to “rerun old arguments”.
In a joint article for The Sunday Telegraph, Mr Baker and Mr Dodds described the situation as “grim” and warned that after January’s 230-vote defeat in the first “meaningful vote”, Mrs May appeared set for another heavy reverse.
“An unchanged Withdrawal Agreement will be defeated firmly by a sizeable proportion of Conservatives and the DUP if it is again presented to the Commons,” they wrote.
Additional reporting by PA