Ambassadors from the 27 other EU countries are also due to hold a meeting in Brussels on Wednesday.
May told the Cabinet earlier Tuesday that "a small number" of issues remain to be resolved in divorce negotiations with the European Union, while her deputy, David Lidington, said the two sides are "almost within touching distance" of a Brexit deal.
Britain wants to seal a deal this fall, so that Parliament has time to vote on it before the U.K. leaves the bloc on March 29. The European Parliament also has to approve any agreement.
Negotiators have been meeting late into the night in Brussels in a bid to close the remaining gaps.
The main obstacle has long been how to ensure there are no customs posts or other checks along the border between the U.K.'s Northern Ireland and EU member Ireland after Brexit.
Irish national broadcaster RTE said the draft agreement involves a common customs arrangement for the U.K. and the EU, to eliminate the need for border checks.
But May faces pressure from pro-Brexit Cabinet members not to agree to an arrangement that binds Britain to EU trade rules indefinitely.
May also faces growing opposition from pro-EU lawmakers, who say her proposed Brexit deal is worse than the status quo and the British public should get a new vote on whether to leave or to stay.
If there is no agreement soon, U.K. businesses will have to start implementing contingency plans for a "no-deal" Brexit — steps that could include cutting jobs, stockpiling goods and relocating production and services outside Britain.
Even with such measures in place, the British government says leaving the EU without a deal could cause major economic disruption, with gridlock at ports and disruption to supplies of foods, goods and medicines.
On Tuesday, the European Commission published a sheaf of notices outlining changes in a host of areas in the event of a no-deal Brexit. They point to major disruption for people and businesses: U.K. truckers' licenses won't be valid in the EU, British airlines will no longer enjoy traffic rights, and even British mineral water will cease to be recognized as such by the EU.
The EU said Tuesday it was proposing visa-free travel for U.K. citizens on short trips, even if there is no deal — but only if Britain reciprocates.
"We need to prepare for all options," EU Commission Vice President Frans Timmermans said. On a deal, he said: "We are not there yet."
Meanwhile, official figures suggest Brexit is already having an impact on the British workforce.
The Office for National Statistics said the number of EU citizens working in the country — 2.25 million— was down 132,000 in the three months to September from the year before. That's the largest annual fall since comparable records began in 1997.
Most of the fall is due to fewer workers from eight eastern European countries that joined the EU in 2004.
Jonathan Portes, professor of economics at King's College London, said the prospect of Brexit "has clearly made the U.K. a much less attractive place for Europeans to live and work."