|The EU's chief negotiator for Brexit Michel Barnier gestures as he gives a speech during the Deutscher Arbeitgebertag congress of German Employers' Associations (BDA) in Berlin. (Tobias SCHWARZ/AFP)
Brussels said it expected more progress on the key issues of the Irish border and the rights of European expats in Britain in order to unlock trade talks at a summit in December.
The EU's chief negotiator Michel Barnier - who met German Chancellor Angela Merkel for Brexit talks - warned that "we are not there yet" but added that he "hopes very quickly, next week, to see that we have found an agreement".
These first signs of a breakthrough have emerged days before British Prime Minister Theresa May is to meet European Commission chief Jean-Claude Juncker in Brussels on Monday, in what the EU says is the "absolute deadline" for an agreement in principle.
London and Brussels have agreed that Britain will up its offer to between €45 and €55 billion (US$53 and US$63 billion), with space for both sides to announce their own final figures, according to the Daily Telegraph.
May said there was no agreement on how much Britain would be on the hook for.
"We're still in negotiations with the European Union," she told the BBC while on a surprise visit to Iraq. "I want a deep and special partnership with the EU in the future."
However, Ireland's EU commissioner Phil Hogan said "The United Kingdom has brought forward proposals that go very close towards meeting the requirements of the EU 27 member states."
"I expect that we will see movement (on Ireland) in the next few days as well," he added.
But there was still work to do. The European Parliament warning, unlike most other parties in the talks who see the matter as closed, that on citizens rights negotiations are "stalled, and even some progress reversed."
Pro-Brexit supporters reacted with anger to divorce bill reports, with leading campaigner Nigel Farage calling the figure "utterly unacceptable".
"For a sum of this magnitude to be agreed in return for nothing more than a promise of a decent settlement on trade represents a complete and total sellout," he wrote in the Daily Telegraph.
Meanwhile, pro-EU Labour lawmaker Chuka Umunna said the government's apparent climbdown was a "whopping great symbol for the impossibility on delivering Brexit on the terms it was sold to the British people."
Investors were more optimistic that the reports heralded a breakthrough, sending the pound 0.4 per cent higher against the dollar, a two-month high.
Foreign Secretary and Brexit campaigner Boris Johnson - who once said the EU could "go whistle" if it demanded a large settlement - on Wednesday appeared to accept the deal if it unlocked the next phase of the talks.
"Now is the moment to get the whole ship off the rocks," he told the BBC during an EU-Africa summit in the Ivory Coast.
An agreement would be a major breakthrough as Britain prepares for an EU summit in December where it is hoping to get the go-ahead to start the next phase of talks on a post-Brexit transition period and future trade ties.
The new British offer comes in two parts. The first concerns May's commitment made in a speech in September that will cover Britain's contributions to the EU budget in 2019 and 2020, even after leaving the bloc.
The second concerns her promise, made in the same speech in Florence, to "honour commitments" made during Britain's four-decade membership, and after going through this line by line, the two sides have reached agreement on the detail.
So far both sides have avoided publicly declaring a clear-cut number for what Britain owes the rest of the EU, but reports and think-tanks put the first part at around €20 billion and the second at €35 billion.
Ministers agreed to boost the offer at a meeting last week.
That leaves the difficult issue of Dublin's EU-backed demand that the frontier with British-ruled Northern Ireland remains open to people and trade.
Hogan echoed the Irish government's position that Britain must make a clear commitment on the "difficult" issue of avoiding a hard border, adding that "we don't hear much detail in relation to how that's going to be achieved."