In her speech on Monday evening, May said: "The negotiations for our departure are now in the endgame".
"We are working extremely hard through the night to make progress on the remaining issues in the Withdrawal Agreement - which are significant", she said.
The content of the deal is presently unknown, but Brexiteers in Parliament have recently expressed concerns that the deal as discussed in Brussels by EU negotiators would be little more than a Brexit in Name Only ('Brino'), with Britain as a rule taker, not rule maker within the Union.
The pound rallied on news of a deal, rising 1.5 percent against the dollar to $1.3038.
The EU wants any withdrawal deal to include a backstop or guarantee that Northern Ireland will remain within the single market after Brexit, but Ms.
Ireland's RTE television reported that the draft deal comprises "one overall backstop" encompassing elements of both the UK-wide and Northern Ireland only arrangements.
Despite the reports, a spokesperson for Simon Coveney, the Irish Foreign Minister, stated the talks were ongoing. "It is clear that although we are making progress, we are not there yet", he told a news conference.
However, after two long days of negotiations on Sunday and Monday, which extended into the early hours of the morning, there is some optimism in Downing Street that a deal could be brokered within the next 24 hours. "The backstop is there as our insurance against big mistakes being made by a future British government".
Mrs May will face resistance from Tory Brexiters like Boris Johnson and Jacob Rees-Mogg who fear that a deal could tie the United Kingdom indefinitely to Brussels, following rules which it has no part in shaping.
However, time is running out to meet the deadline for a November EU summit. "This will not be an agreement at any cost".
Brexit secretary Dominic Raab is preparing to lead a group of Cabinet ministers arguing that a no-deal exit would be preferable to a deal that breaches their red lines.
The government doesn't usually release legal advice it gets, but Labour is using a "humble address", the same device it used a year ago to get Brexit economic-impact studies released.
The agreement is meant to finalise Britain's exit bill of around £39 billion (45 billion euros, $50 billion), guarantee citizens' rights and launch a 21-month transition, during which London will follow European Union rules.
It must also guarantee citizens' rights and launch a 21-month transition during which London will follow European Union rules.
In the transition period, British and European negotiators will launch more ambitious talks to agree the future trading and legal relationship.
Brussels wants to get agreement on a draft deal by the end of Wednesday at the latest if there is to be a summit this month to approve it, although few in Brussels seemed to hold out much hope that a breakthrough could come this week.