With trade talks between the two sides going to the wire following another weekend of talks, the two leaders will see if a deal can be salvaged after their top negotiators Lord Frost and Michel Barnier spent Sunday locked in detailed talks.
On Sunday it appeared there had been a breakthrough on the thorny issue of future fishing rights, after EU sources briefed journalists, but the UK rubbished the reports, with a government source saying "there’s been no breakthrough on fish. Nothing new has been achieved on this today".
With the Brexit transition period ending at the end of December, there are fears time is running out to prevent potentially disastrous impacts on the UK.
Minister James Cleverly told ITV News it is "impossible to predict" whether a deal will be reached before the end of the year, with a "small number of significant points" still yet to be agreed.
He said "time is tight" but negotiators "will keep working" towards reaching a deal.
Asked whether MPs would be expected to sit in Parliament through the Christmas period in order to ratify a deal, if one is reached, the minister said "it's reasonable to expect Parliament to work hard to get that through".
On Sunday, ITV News Political Editor Robert Peston detailed a "reasonable worst case scenario", documented in the government's planning assumptions.
Among the potential effects are a reduction in medicine supply and a rise in food and fuel costs.
Citing Peston's report, Good Morning Britain's Piers Morgan asked Cabinet minister Cleverly if this is the government's position.
"When I was a minister at DExEU (Department for Exiting the EU) I lost track the number of times I had to explain what a reasonable worst case scenario document is," he said.
"It is not a prediction, it is not saying what will or is even likely to happen, it is a document that describes the worst case scenario to allow governments to plan mitigations.
"In the same way that a seat-belt is a mitigation for a reasonable worst case scenario that you have an accident in your car."
The talks were due to continue in Brussels on Monday after Mr Barnier has briefed a breakfast meeting of ambassadors from the 27 EU member states on the state of play.
EU negotiators are reported to be insisting on a “ratchet clause” under which the UK would face additional tariffs if it failed to mirror changes to EU rules on issues like environmental standards and workers’ rights.
Michael Gove will also head to Brussels to discuss the controversial clauses in the Internal Market Bill.
Following their earlier call on Saturday, Mr Johnson and Mrs von der Leyen acknowledged that there were still “serious differences” to be resolved on fisheries and the mechanism for resolving disputes as well as competition rules.
While the two sides have been circling round the same issues for months, it is unclear whether the intervention of the leaders has created the political space for the negotiators finally to bridge the gap.
What is agreed is that time is rapidly running out.
If there is no deal by the end of the Brexit transition period at the end of the month, then Britain will leave the single market and the customs union and begin trading with the EU on World Trade Organisation terms, with the imposition of tariffs and quotas.
Brexit trade talks - the sticking points at a glance:
- Fishing rights: The UK wants total control over its own fishing waters after the Brexit transition period ends, with a 12 mile exclusion zone around the British Isles banning all foreign vessels. The EU wants the UK to stick to the Common Fisheries Policy, an EU agreement which gives member nations the rights to fish in European waters - more here.- Level Playing Field: This is a concept all EU nations agree to, which ensures member nations cannot undercut others by setting their own rules on issues such as the environment, taxation and state aid. The EU says a zero-tariff trade deal is dependent on the UK agreeing to a level playing field. The UK disagrees, saying a fundamental aspect of Brexit is that the UK will be able to set its own rules.- Governance of a deal: It's likely that any trade deal will eventually result in disputes. The EU wants the European Court of Justice to be the final authority in ruling over disputes. The UK says the ECJ should have no role and final decisions should be made by a bespoke arbiter.
Before then it has to be ratified by both Houses of Parliament in the UK and the European parliament as well as signed off by the EU leaders.
There had been hopes that could happen at a two-day summit in the Belgian capital starting on Thursday – their final scheduled gathering of the year – but the timetable is looking increasingly tight.
France has publicly warned that it will veto any deal if it is unhappy with the terms, amid signs President Emmanuel Macron is anxious that Mr Barnier is preparing to give too much ground in his determination to get a deal.
Meanwhile, the mood around the negotiations is unlikely to be improved by the government’s decision to bring back to the Commons legislation enabling ministers to override elements of the “divorce” settlement with Brussels in breach of international law.
It means that on Monday – when Mr Johnson and Mrs von der Leyen are due to be speaking – MPs will vote on whether to overturn amendments by the House of Lords which removed the provisions in the UK Internal Market Bill relating to the Irish border.
On Wednesday, MPs will then go on to consider the Taxation (Post-Transition Period) Bill which contains further similar provisions, which have infuriated the EU.