EU chief Brexit negotiator Michel Barnier is in Dublin for talks with Taoiseach (Irish PM) Leo Varadkar.
A spokesman for Mr Varadkar said the aim of the meeting was to “take stock of developments in London”.
The spokesman said the ongoing planning for a possible no-deal scenario would also be discussed.
The UK is currently due to leave the EU on 12 April and, as yet, no withdrawal deal has been approved by MPs.
Prime Minister Theresa May has been negotiating with Labour to try and reach a deal in Parliament.
She is due to meet German Chancellor Angela Merkel and French President Emmanuel Macron on Tuesday.
During his Dublin visit, Mr Barnier will also meet Irish Foreign Affairs Minister Simon Coveney and Finance Minister Paschal Donohue.
Mr Coveney said it was not surprising that Mr Barnier would visit Dublin before the EU summit on 10 April, where leaders will discuss any plan to delay the UK’s departure.
“What he will want to do first of all is show solidarity with Ireland,” Mr Coveney told Irish broadcaster RTÉ.
“But also I think he’ll want a detailed conversation in terms of Ireland’s perspective on the most recent ask from the prime minister for an extension of time.
“Ireland is of course willing to give the process more time, but we, like many other EU member states, will want to see a plan to go with that to show that there is a proposed way of finding a majority support in Westminster for a way forward.”
Asked about Ireland’s position on Mrs May’s request to delay Brexit until June 30 versus a possible flexible one-year extension, Mr Coveney said: “We’re open to either in truth.”
“As long as there is a credible plan in order to get a deal across the line, then I think European leaders will look at an extension positively.
“But they will need to see a credible plan to go with the ask.”
The visit comes after Mr Varadkar held bilateral meetings with French and German leaders.
The German Chancellor Angela Merkel said on Thursday that Germany will stand with Ireland “every step of the way” over Brexit.
Following talks with Mr Varadkar at the beginning of April, French President Emmanuel Macron said: “We will never abandon Ireland or the Irish people no matter what happens, because this solidarity is the very purpose of the European project.”
Meanwhile Sinn Féin President Mary Lou McDonald and Vice-President Michelle O’Neill are due to hold a series of meetings in London with senior British politicians on Brexit.
Key dates in the week ahead
- Monday: Possible resumption of talks between the government and Labour
- Wednesday: Emergency summit of EU leaders to consider UK request for further extension until 30 June, with the option of an earlier Brexit day if a deal can be agreed
- Friday: Brexit day, if UK is not granted a further delay