The Prime Minister will meet Ursula von der Leyen, the European Commission President, for a summit that could define not only his premiership but Britain’s place in the world for decades to come.
Both sides said that “significant differences” remain, and British officials said that while Mr Johnson would not be making the trip if he did not think a deal could be agreed, “things are looking very tricky”.
EU sources speculated that while Mr Johnson’s trip could end in a deal, it might also be intended purely to show that he tried everything he could to get a deal even if he expects to come home empty-handed.
Mr Johnson could travel to Brussels as early as Wednesday, ahead of a summit of EU leaders on Thursday. It would leave open the possibility that he could stay on in Belgium to arrange meetings with key players including Angela Merkel and Emmanuel Macron in order to appeal to them directly.
Another option under discussion is a meeting with Ms von der Leyen at the weekend, after the European Council meeting is over, which would give EU leaders the chance to agree a new mandate for the Commission President before she meets Mr Johnson.
The Prime Minister has long believed Thursday’s summit – which he cannot attend because Britain has now left the EU – could hold the key to unlocking the logjam around fishing, so-called level playing field guarantees, and the governance of any deal.
A British source close to the negotiations told The Telegraph: “We definitely still think a deal could be done but it’s increasingly possible that it might not.
“We are in the same place as we were on Friday evening. It hasn’t got any worse, but it hasn’t got any better either.
“We have reached the end of the road on what can be achieved in this format at this level with the negotiating teams, and decisions will have to be taken at a political level now.
“The meeting between the Prime Minister and the Commission President will not be window-dressing. They will have to do some negotiating themselves.”
Mr Johnson will be taking a huge gamble by entering the lion’s den in Brussels for the first time since he became Prime Minister, an arena that both Theresa May and David Cameron failed to conquer, to their ultimate cost.
However, Downing Street insisted Mr Johnson is entirely prepared to walk away without a deal, and has been at pains to downplay expectations.
A senior Government source said: “We have made no tangible progress. It’s clear this must now continue politically.
“Whilst we do not consider this process to be closed, things are looking very tricky and there’s every chance we are not going to get there.”
Mr Johnson and Ms von der Leyen spoke for over an hour by phone on Monday, in a call that did not involve any negotiations but allowed them to “take stock” of what the talks had and had not achieved.
Mrs von der Leyen, Angela Merkel, Emmanuel Macron and Charles Michel, the European Council president held a videoconference to prepare for Thursday’s EU summit in the afternoon, before the call with the Prime Minister.
In a joint statement, the two leaders said: “We agreed that the conditions for finalising an agreement are not there due to the remaining significant differences on three critical issues: level playing field, governance and fisheries.
“We asked our chief negotiators and their teams to prepare an overview of the remaining differences to be discussed in a physical meeting in Brussels in the coming days.”
Michel Barnier, the EU’s chief negotiator, had earlier told EU ambassadors that Wednesday was the final deadline for a deal to be agreed, but Downing Street would only say an agreement had to be reached “this week”.
The pound, which had fallen by more than one per cent against the dollar over the course of the day, rallied after the announcement of Mr Johnson’s trip to Brussels as traders interpreted it as a sign that a deal had become more likely.
The Prime Minister held out an olive branch to the EU by confirming he is prepared to withdraw a threat to break the terms of the Brexit divorce deal.
Downing Street signalled its willingness to scrap contentious clauses contained in the UK Internal Market Bill (which is continuing its passage through Parliament this week) that protect trade between Great Britain and Northern Ireland, if other solutions can be agreed.
The clauses have drawn fierce criticism in Brussels and the House of Lords because they override the Withdrawal Agreement, thereby breaching international law in what ministers have described as a “specific and limited way”.
If a trade deal is agreed ministers “would be prepared to remove” or “deactivate” the controversial clauses, No 10 said in a statement.
Last month, peers voted to remove them from the Bill, but Downing Street re-inserted them when the legislation returned to the Commons, a move significantly softened by the Government’s offer to pull them at a later date.
In a second move aimed at easing tensions with the EU, the Government delayed publishing another Bill that was set to include similar clauses breaching international law.
The Taxation Bill was initially due to be published by early afternoon, but the timetable was pushed back until Tuesday. The Government announced it would “keep under review the content” of the Bill.
Simon Coveney, Ireland’s foreign minister, said member states were steeling themselves for a no deal outcome.
He said: “Many of the ministers I spoke to today are just getting increasingly frustrated and increasingly resigned to the fact that there may be no deal…
“In Brussels certainly the mood is starting to shift to contingency planning for a no deal.
“The next two days need to be very different to the last two days.”
One EU diplomat said: “Political intervention won’t do anything when the positions are still heavily guarded.
“Perhaps there is a choreography leading to this special summit. However, on the fundamentals I have not seen anything change and basically nothing has altered for the last eight weeks so I’m in the dark what would now suddenly move which didn’t before.”
Some EU member states believe the negotiations could even carry on beyond this weekend.
Stef Blok, Dutch foreign minister, said: “I hope the talks don’t collapse tonight. It’s the 7th of December and not the 1st of January. As far as I am concerned, we should use the time it takes to negotiate and not allow ourselves to be rushed into a hasty compromise.”
Paymaster General Penny Mordaunt told the Commons the level playing field issue, which would force Britain to mirror future changes in EU rules and regulations, “is currently the most difficult.”
She said: “We are all working to get a deal, but the only deal that is possible is one that is compatible with our sovereignty and takes back control of our laws, trade and waters.
“While an agreement is preferable, we are prepared to leave on so-called Australian-style terms if we can’t find compromises.”
An EU diplomat said: “We are now entering the endgame of the endgame. The stakes couldn’t be higher. Let”s hope that Prime Minister Johnson puts Britain’s long-term interests first. In this case a deal will still be possible.”