An urgent hearing will be held by Europe's top court on Tuesday over whether Britain can unilaterally reverse its decision to leave the EU, in a case supporters of "remain" hope could pave the way for a second referendum and ultimately stop Brexit.
May's Tuesday tour includes meetings with political leaders from all parties in Northern Ireland - which will have Britain's only land border with the EU and whose future has been a stumbling block in the negotiations.
Yet concerns are not just pervaded in the European continent. The U.S. is also worrying if the package would potentially hurt the trade ties between the two sides.
U.S. President Donald Trump said on Monday the agreement allowing the UK to leave the EU may make trade between the U.S. and Britain more difficult, but the UK prime minister's office disputed his interpretation.
Trump told reporters outside the White House that the deal sounded like it would be good for the EU, but "I think we have to take a look seriously whether or not the UK is allowed to trade."
"Because right now if you look at the deal, they may not be able to trade with us," he said. "And that wouldn't be a good thing. I don't think they meant that."
He said he hoped May would be able to address the problem, but he did not specify which provision of the deal he was concerned about.
A spokesperson for May's office said the agreement struck with the EU allowed the UK to sign trade deals with countries throughout the world, including with the U.S.
"We have already been laying the groundwork for an ambitious agreement with the U.S. through our joint working groups, which have met five times so far," the spokesperson said.