Prime Minister Theresa May's deputy says Britain and the European Union are "almost within touching distance" of a Brexit deal after another late-night negotiating session.

Cabinet Office Minister David Lidington says it's "possible but not at all definite" that the two sides can reach agreement this week.

Britain wants to seal a deal this fall, so that Parliament has time to vote on it before the United Kingdom leaves the bloc on March 29.

The European Parliament also has to approve any agreement.

Negotiators have been meeting late into the night in Brussels in a bid to close the remaining gaps.

May's cabinet is meeting on Tuesday for an update.

Differences remain between Britain and the bloc over how to ensure the border between Northern Ireland and Ireland remains open after Brexit.