Mr Davis, Brexit Secretary, travelled to Brussels ahead of the second round of formal talks with the EU’s chief negotiator Michel Barnier over the UK’s departure from the EU, The Financial Times reported.
At a brief press conference with Mr Barnier earlier in the morning, the Brexit secretary said that this week’s talks will focus on citizens' rights, finance and "other separation issues", with separate negotiating teams set up for each.
Issues relating to Northern Ireland will also be addressed, with Mr Davis - who has returned to London - and Mr Barnier expected to give an update on the progress made in a press conference on Thursday.
David Davis said his priority was to "lift the uncertainty" for EU citizens living in the UK and Britons living in the EU.
Mr Barnier said the negotiators would "now delve into the heart of the matter".