The holdup surrounds a failure to secure sufficient support from senior ministers, with Downing Street hoping to publish the document on Thursday after briefing Brussels on its content.
Mrs May’s new arrangement plans to keep the UK remaining closely tied to the EU for an indeterminate period of time at the end of the transition period in the hope a new customs fix would emerge as the answer for the Irish border question.
Preventing a hard border on the island of Ireland has become Brexit’s most divisive topic, with Irish prime minister Leo Varadkar warning the issue could derail the whole process.
The Prime Minister’s plans to keep the UK aligned to Brussels for an indefinite period is her latest attempt at winning over the EU27, but has faced domestic stumbling blocks while trying to the win support of her so-called Brexit war Cabinet.
David Davis is at the heart of the blockage with his refusal to backdown and a demand for a time-limited plan. The disagreement has sparked rumours that the Brexit Secretary is planning a shock resignation, however, sources close to the senior minister have denied any possibilities of quitting office.
Other Brexiteers are also preparing to confront the Prime Minister at a meeting of her Brexit war Cabinet on Thursday.
Former Brexit minister David Jones has warned the UK’s EU divorce would become “deeply dangerous” without his former boss Mr Davis at the helm.
Mr Jones told the BBC: “Negotiations continuing without David Davis would be deeply upsetting and deeply dangerous for the country.
“David Davis needs to stay where he is.”
Meanwhile, in Brussels, EU officials are happy to let the drama in Westminster play out while they wait for any proposals to arrive on the negotiating table.
The EU’s team had expected the document to be at least presented to them on Wednesday as part of the week’s negotiations.
However, even if Mr Davis is able to convince the Prime Minister to offer a time-limited Brussels would likely turn it down.
An EU official said: “you’re leaving unanswered the question of what happens in, say 2023, or whenever it expires. The idea is to avoid that.”
While things are moving on in negotiations, the EU’s hopes for the June summit, where leaders of the EU28 will meet, have been significantly scaled back with many resigned the Irish border debate will rumble on into October.
Nonetheless, the EU’s chief negotiator Michel Barnier is expected to hold a public briefing on Friday before Mr Davis travels to Brussels on Monday for a private meeting with his counterpart.
The Frenchman is likely to treat Friday’s address as a “soft landing” for any proposals ahead of the June summit.
Mrs May has held “constructive” talks with Mr Davis and expects him to remain in his post, Downing Street has said.
The Prime Minister also held separate face to face meetings with Foreign Secretary Boris Johnson and International Trade Secretary Liam Fox.
The meetings took place in her parliamentary office, the one with Mr Davis was the longest, believed to have run to more than 30 minutes.