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.
The BBC’s Laura Kuenssberg said it was not now clear whether there would be a deal at all this week.
Boris Johnson has been trying to get Tory Brexiteers and the DUP to back his revised plan for Northern Ireland.
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”.
‘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.
The party’s leader, Arlene Foster, held talks in Downing Street on Tuesday night and Wednesday morning.
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.”
Analysis: Nick Eardley, BBC political correspondent
Conservative Brexiteers want to believe Boris Johnson – they trust him, but they have not seen the legal text of a deal, so they are not saying definitively “yes, we will vote for it.”
The most important players are the DUP. We think they are seeing the PM again tonight and those conversations could be crucial.
If the DUP fall in behind him then it seems that Boris Johnson would have the numbers to get a deal over the line.
But if they don’t, it is very hard to see how he could do it.
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.