There will not be a finalised Brexit deal today, BBC political editor Laura Kuenssberg reported, citing an unnamed UK government source.
"A government source has just told me there will not be a deal tonight," she said in a tweet, with European Union sources saying that Britain and the EU were on the verge of a deal.
She added: "Simply not clear if that means there's no way forward yet or just a case of extending talks into tomorrow (because) they need a bit more time."
The political editor of The Sun newspaper also said there would be no Brexit deal on Wednesday (Thursday NZT). He added that there were unresolved issues with both the EU and the Northern Irish Democratic Unionist Party (DUP) who support the Conservative minority government in Britain's parliament.
"Everyone will be working into the night but there won't be a deal this evening," Tom Newton-Dunn quoted a government source as saying.
The EU's Donald Tusk said he would have "bet" on a deal 24 hours ago, but "doubts" had appeared on the UK side.
The PM is trying to get Tory Brexiteers and Democratic Unionists on board for his revised plan for Northern Ireland.
Likening talks to climbing Everest, Mr Johnson said the summit was "not far" but still surrounded by "cloud".
He is in a race against time to get a deal before Thursday's (Friday NZT) crucial EU council meeting.
The BBC's political editor Laura Kuenssberg said she understood the issues between the UK, EU and Ireland were "pretty much sorted", but it was still not clear whether the Northern Irish DUP were ready to sign up or not.
Mr Johnson has been updating his cabinet on the state of the negotiations after further talks with the DUP, whose support could be vital if Parliament is to approve any agreement.
The PM also briefly addressed a meeting of Conservative MPs, comparing the current position to Edmund Hillary's ascent of Mount Everest in 1953.
The EU's chief negotiator, Michel Barnier, has just begun to brief EU ambassadors on the status of the talks - the meeting was originally due to take place at lunch time but was put back twice.
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.
The backstop - the solution to border issues agreed by Theresa May - proved unpalatable to many MPs so Mr Johnson has come up with new proposals to dispense with it.
However, they would see Northern Ireland treated differently from the rest of the UK - something the DUP, among others, has great concerns about.
The BBC's Brussels reporter, Adam Fleming, said that during the course of Wednesday there had been a shift in emphasis in the talks away from issues around customs towards matters surrounding 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 DUP is understood to be most concerned about this issue too. The party also fears the creation of a "customs border" in the Irish Sea, which would require checks on goods between the rest of the UK and Northern Ireland.
The DUP held their latest round of talks in Downing Street on Wednesday morning. After a 90-minute meeting on Tuesday, they said "it would be fair to indicate gaps remain and further work is required".
Party leader Arlene Foster dismissed suggestions that their concerns had since been allayed.
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.
One senior EU diplomat has told journalists in Brussels it is now too late for EU leaders to formally approve a revised Brexit deal at the summit.
They said the most they could do was give a provisional thumbs-up - "a political yes" - to whatever emerges from the talks pending the release of the final legal text.
- BBCand Reuters