The two men will begin talks on the post-Brexit transitional arrangements.
Potential sticking points include citizens’ rights, with the UK insisting EU nationals arriving during this time should not have the same rights as those who arrived before Brexit day.
It is the first time the two have met in London and marks the start of a key week in the ongoing Brexit talks.
EU sources are keen to hear the UK reaction to the EU’s negotiating directive.
UK Prime Minister Theresa May is also expected to take part in the talks in London.
Meanwhile, key UK cabinet colleagues will meet on Wednesday and Thursday to decide the details of the UK government’s policy regarding a customs union.
No breakthroughs are expected by the EU side, though they desperately hope the UK will be ready to work on the text of a final exit deal soon.
At the weekend, May categorically ruled out keeping Britain in any form of customs union with the EU in a significant victory for Brexiteers, ahead of the two crucial cabinet meetings this week.
On Sunday, Downing Street said it wanted to “put to rest” arguments that have raged for weeks about whether the UK would join a customs union after Brexit.
British Home Secretary Amber Rudd said on Sunday that the UK “wants to have tariffs at the border so that is a form of customs agreement, arrangement, partnership,” but, “It is likely to have something within the customs framework.”
In a position paper published in August, the UK set out two potential options for future long-term customs operations.
A “partnership” arrangement would see the UK “align precisely” with the EU in terms of imports and exports, removing the need for any customs checks between the two.
The UK would continue to operate its own checks on goods coming from outside the EU - and safeguards would be needed to prevent goods entering the EU that had not complied with its rules.
An alternative scenario would involve the UK extending customs checks to EU arrivals but under a “highly streamlined arrangement” to minimise disruption at ports and airports
Elsewhere, Nick Clegg, a former MEP and ex-Liberal Democrat leader is expected to use a speech in Brussels on Monday to say that the UK could stay within limited form of EU membership.
Clegg’s speech coincides with the latest round of Brexit talks.
Clegg is expected to say that Brexit can and should be stopped if it fails to bring voters the benefits promised to them by leave campaigners.
He has previously said MPs were “duty bound” to reject a poor deal.
He will speak at an event organised by the Lisbon council and Radix.
The event, ‘The Future of Europe - How a radical centre can deliver a continent of reform and renewal’ will take place at Résidence Palace.