The issue of the Northern Ireland "backstop", the contingency plan in place to avoid a hard border, is thought to have been the main point of discussion at the meeting.
Britain's global trade, environment and Brexit ministers told May at a meeting on Thursday that they fear the whole of Britain could remain in the EU customs union for an open-ended period, the BBC said.
"This is critical", Nigel Dodds, deputy leader of the Democratic Unionist Party (DUP) which props up Theresa May's government, said on Twitter.
"The Government has yet to admit that a no-deal would require a raft of substantial legislation to be rushed through Parliament, crucial stop-gap agreements with the European Union on matters relating to Northern Ireland and security, and the recruitment of thousands of customs officials", said Sir Keir.
According to the BBC, Brexiteers were particularly concerned over the fact that Britain could be tied to the bloc's mechanisms indefinitely, which would become an obstacle to the country's independent trade deals elsewhere once it leaves the EU.
'There would appear to be progress, but sometimes the devil is in the details, ' she said.
"But it is true that there needs to be a period, probably following the transition period that we have negotiated, before we enter into our long-term partnership, just because of the time it will take to implement the systems required", he said.
Earlier, Work and Pensions Secretary Esther McVey, who was not at the Downing Street meeting, refused to endorse the prime minister's blueprint for Brexit.
While the UK's Parliament and general public debate how to implement the country's withdrawal from the European Union and how to define its relationship with the bloc, a new report highlights one area in which the nation is already seeing a decline: its attractiveness as a destination for clinical trials.
They indicated the collapse of negotiations could threaten electricity blackouts in Northern Ireland, disrupt Channel Tunnel rail services and cost the United Kingdom free trade agreements with more than 70 non-EU countries around the world. Negotiators were also sparring over whether that would cover Northern Ireland or mainland Britain as well.
The DUP, on whose support Mrs May depends for a working parliamentary majority, is hostile to the customs plan, arguing it could lead to checks on goods moving between Northern Ireland and the rest of the United Kingdom.
"I fully appreciate the risks of a "no deal" (Brexit) but the dangers of a bad deal are worse", Foster wrote in an article in the Belfast Telegraph published on Saturday.