Ahead of the meeting with EU leaders on Monday, the Prime Minister has admitted she has yet to resolve the Irish border problem.
Despite attempts to find a solution over the weekend, there has not been sufficient progress on avoiding a hard border.
In the first round of Brexit talks, May will meet with European Commission president, Jean-Claude Juncker on Monday to discuss the Irish border, citizens’ rights and the financial settlement.
Without progress, the Prime Minister will not be able to advance talks to the second phase.
Ireland’s deputy Prime Minister suggested over the weekend that a finalised deal did not have to be made this weekend.
“We’re not looking for the full detail of the border solution in phase one of these negotiations,” he said.
“We’ve never asked for that. What we are looking for though is the parameters within which we can be more confident that a solution can be found within phase two.”
May has a deadline, which is on 4 December, when EU leaders decide if talks can take the next step to phase two.
Following the weekend of talks, an Irish official said that a final agreement had not yet been reached.
“Contacts continue at official level in order to reach an agreement. There is still a way to go. There must be clarity on the need to avoid regulatory divergence which would lead to the re-emergence of a border.”
“A positive outcome to the talks between UK PM May and President Tusk and President Juncker will be very important if we are to make the progress necessary before the European Council,”
May has faced widespread criticism about her Brexit approach. Conservative Brexiters have made clear how they feel with compromises she has made in talks so far.
Former cabinet minister, Iain Duncan Smith, wrote in the Sunday Telegraph this week that he strongly opposed a plan for the ECJ to have an ongoing role, beyond the transition period.