The Prime Minister will also meet the other Northern Ireland parties, the SDLP, the Ulster Unionists and the Alliance.
The newspaper said Britain wanted these rights to be available only to those European Union nationals who were living in the country before March 29 this year, when the government triggered the start of the two-year process of leaving the EU.
During the appearance, Ms O'Neill said: 'We made very clear to the prime minister that any deal between herself and the DUP can not undermine the Good Friday agreement.
On a visit to Paris on Tuesday evening where she met with French President Emmanuel Macron, May described the talks as "productive".
May took up her familiar refrain, arguing the deal is vital to "give the stability to the UK Government that I think is necessary at this time". May's office issued a statement saying she was "deeply saddened by the tragic loss of life" but made no mention of the talks with the DUP.
May has dismissed calls to resign following the dismal election result after calling a vote three years early in the hope of bolstering her slim majority ahead of the Brexit talks.
The EU will keep the door open for Britain to return, but only on worse terms than it now has, European Parliament Brexit negotiator Guy Verhofstadt said Wednesday.
The unionists have struggled for years with Irish Catholic nationalists who want Northern Ireland to join a united Ireland.
During the campaign, May cast herself as the only leader competent enough to navigate the tortuous Brexit negotiations that will shape the future of the United Kingdom and its $US2.5 trillion ($A3.3 trillion) economy.
It follows warnings - including from former prime minister Sir John Major - that the Government will compromise its stated impartiality in the province if it enters a confidence and supply deal with the DUP at Westminster.
The Conservatives are considering an arrangement in which the Northern Ireland party backs May on the budget and her confidence motions.
Barnier held "talks about talks" with May's Brexit advisor Olly Robbins and British EU Ambassador Tim Barrow in Brussels on Monday but they failed to agree on a date for the negotiations to begin, an EU official said.
May has promised to start the formal Brexit talks next week but opponents of a sharp break with the European Union took her woes as a chance to push back against her strategy.
As European leaders tried to fathom exactly how Britain would begin the negotiations, German finance minister Wolfgang Schaeuble said Germany wanted a Brexit deal that would limit negative consequences for the bloc but also did not want it to weaken Britain.