Northern Ireland and the Irish border are due to be discussed at the Brexit negotiations in Brussels on Wednesday.
Brexit Secretary David Davis said UK and EU negotiators will be "crunching through the technical detail" of the Good Friday peace agreement and the Common Travel Area (CTA).
The CTA allows passport-free travel between the UK and the Irish Republic.
The UK and the EU agreed at the last round of talks that they had made good progress on preserving the arrangement.
However, they also said more work is needed on mapping out all of the different cross-Irish-border relationships and how Brexit could affect them.
In a speech last week, the prime minister restated that there will be no physical infrastructure at the Irish border after Brexit.
Theresa May said that both the UK and the EU have "stated explicitly" that they will not accept any physical infrastructure at the border.
That is in spite of the UK leaving both the customs union and the single market.
The EU's chief negotiator Michel Barnier said Mrs May's speech had not clarified "how the UK intends to honour its special responsibility for the consequences of its withdrawal for Ireland".
The Irish Prime Minister Leo Varadkar met Mrs May on Monday and said he had encouraged her to be "more specific" about how she sees the future UK-Irish relationship.
His government would like the UK to stay in a customs union with the EU, seeing that as the best way to avoid a so-called hard border.