Sinn Fein's Stormont leader, Michelle O'Neill, said she would raise the issue with the Prime Minister in face-to-face talks in London on Thursday.
Talks between the Tories and the Democratic Unionist Party were continuing on Wednesday amid reports that any announcement of a deal may be delayed because of the tragic fire in a London tower block.
May's office said Northern Ireland's five main parties would take part, but a spokesman for the DUP did not immediately respond to a request to confirm their participation.
"The danger is that however much the government tries, they will not be seen to be impartial if they are locked into a parliamentary deal in Westminster with one of the Northern Ireland parties", Major said.
The European Parliament's Brexit negotiator, Guy Verhofstadt, also expressed his frustration.
On a visit to Paris on Tuesday evening where she met with French President Emmanuel Macron, May described the talks as "productive".
"The first phase of the negotiations will tackle three main areas: safeguarding the rights of citizens, financial settlement of the UK's obligations and the new external borders of the European Union", the Commission said. "But like in Alice in Wonderland, not all the doors are the same", he added. "It will be a brand new door, with a new Europe, a Europe without rebates, without complexity, with real powers and with unity". "Delay to deal with DUP means likely postponement of Queens speech; and possibly Brexit talks", BBC political reporter Norman Smith said on Twitter. "We will be asking the prime minister to be open with politicians and also with the public", SDLP leader Colum Eastwood said in a statement.
Yet many of her lawmakers and party members favour a sharp break with the European Union - a sign of the divisions over Europe that helped sink the premierships of May's predecessors Margaret Thatcher, John Major and Cameron.
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. However, this is not a short term solution and the case could be dragged on for years.
The EU will open the historic divorce talks with the United Kingdom by discussing the size of the bill London will have to settle, the rights of EU and UK citizens and the bloc's new external border in Northern Ireland. Major, who helped to bring about that peace, said he was concerned that May's arrangement with the DUP could pitch the province back into turmoil by persuading "hard men" on both sides of the divide to return to violence.