Image copyrightAFPImage captionBoris Johnson has been holding meetings with parliamentary factions he hopes will back any deal he reaches
A government source has told the BBC there will be "no deal tonight", as officials continue to work on the technical details in Brussels.
The UK and EU had been hoping to sign off a revised Brexit deal before Thursday's crunch EU council meeting.
Boris Johnson has been trying to get Tory Brexiteers and the DUP to back his revised plan for Northern Ireland.
The new draft Brexit deal has a mechanism enabling Northern Ireland to approve or reject the border plans.
This would give the Stormont Assembly the chance to vote on Brexit arrangements four years after the transition period ends in 2020.
The EU believes this replaces the controversial Northern Ireland backstop with arrangements that are sustainable over time and are democratically supported, as requested by the UK.
The backstop was designed to avoid a hard border on the island of Ireland after Brexit and involved the UK potentially retaining a very close relationship with the EU - staying in the customs union - for an indefinite period.
The legal text of the draft still has to be approved by the British government.
BBC political editor Laura Kuenssberg said she understood the issues between the UK, EU and Ireland were "pretty much sorted", but that DUP sources were warning there were still gaps between proposals and what the party could support.
The Democratic Unionist Party has propped up the Conservative government since the 2017 general election and their support could be vital if Parliament is to approve any agreement Mr Johnson secures.
Earlier, the PM likened the Brexit talks to climbing Everest, saying the summit was "not far" but still surrounded by "cloud".
He will travel to Brussels to attend the EU Council summit on Thursday.
'We are working'
The UK is due to leave the EU at 23:00 GMT on 31 October and Mr Johnson has repeatedly insisted this will happen, regardless of whether there is a deal or not.
The EU's chief negotiator Michel Barnier has, meanwhile, been briefing EU ambassadors, ahead of Thursday's summit - the meeting was originally due to take place at lunch time but was put back twice.
Asked afterwards, whether there was a deal, Mr Barnier said: "We are working, we are working."
The issue of the Irish border - and how to handle the flow of goods and people across it once it becomes the border between the UK and the EU after Brexit - has long been a sticking point in the negotiations.
The border is also a matter of great political, security and diplomatic sensitivity in Ireland.
Mr Johnson's proposals for a new Brexit deal hinge on getting rid of the backstop - the solution to border issues agreed by Theresa May which proved unpalatable to many MPs.
However, his plans would see Northern Ireland treated differently from the rest of the UK - something the DUP, among others, has great concerns about.
The DUP has, in particular, been demanding assurances around the so-called consent mechanism - the idea the prime minister came up with to give communities in Northern Ireland a regular say over whatever comes into effect.
A source told Newsnight's political editor Nick Watt the thinking in Number 10 was that "the DUP never want to own a solution - at some point you have to call their bluff. You just have to hope they will sulkily acquiesce."
The party's leader, Arlene Foster, held talks in Downing Street on Tuesday night and Wednesday morning.
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As well as the DUP, Mr Johnson is also trying to secure support from Tory Brexiteers, most of whom are part of the European Research Group.
Chairman Steve Baker told reporters after a meeting in Downing Street on Wednesday evening his group "hope [to] be with the prime minister, but there are thousands of people out there who are counting on us not to let them down and we are not going to".
"We are just really wishing the prime minister well and hoping he has total success. We know there will be compromises, but we will be looking at this deal in minute detail with a view to supporting it, but until we see that text, we can't say."
As Wednesday draws to a close, a deal is still, DBP - difficult but possible, in case you haven't caught the lingo by now.
I hear from both sides of the Channel that the issues between the UK, Ireland and the EU are pretty much ironed out.
A schedule is in place for EU leaders to be able to sign off a deal tomorrow, discussing it as the first item on the agenda at the summit if the ink is dry.
The government has in place its plan to ask MPs to approve the hypothetical deal in Parliament on Saturday.
Despite all the obstacles, all the warnings about the tightness of the timetable, it is not yet too late.
Boris Johnson faces another deadline on Saturday - the date set out in the so-called Benn Act, which was passed last month by MPs seeking to avoid a no-deal Brexit.
If MPs have not approved a deal - or voted for leaving the EU without one - by Saturday, then Mr Johnson must send a letter to the EU requesting an extension to 31 January 2020.
The prime minister's official spokesman has confirmed the government will table a motion for Parliament to sit this Saturday from 09:00 to 14:00 BST.
That motion would be considered on Thursday.
However, this does not mean the House of Commons will definitely sit on Saturday - the government could table the motion but not push it to a vote.
And the picture in Brussels
The expectation on the EU side is that a new Brexit deal text is pretty much ready.
They are now just waiting to hear from the UK side whether it can be signed off.
Even if this text is ready, though, even if it can be signed off by EU leaders, the EU will not yet be breathing a sigh of relief because they have been here before.
Theresa May signed a Brexit deal with the EU and it went on to be rejected multiple times by House of Commons.
The fear is, if a new Brexit text meets the same fate, the UK government will come back to Brussels asking for more concessions.
