"I would welcome very much the fact that the United Kingdom has brought forward proposals that go very close towards meeting the requirements of the EU 27 member states," said Agriculture Commissioner Phil Hogan.
London and Brussels have agreed that Britain will pay between 45 and 55 billion euros ($53 and $63 billion), according to the Daily Telegraph.
The Financial Times reported Britain would cover EU liabilities worth as much as 100 billion euros, but when structured as net payments over many decades that could drop to less than half that amount.
EU chief negotiator Michel Barnier warned that "we still have work to do, the negotiation is not over on this subject" but voiced hope that an agreement could be struck next week.
- 'Cautiously optimistic' -
British Treasury minister Liz Truss also told parliament that "nothing is agreed until everything is agreed".
An EU diplomat told AFP that they were aware of the "rumours" but that "we are waiting to see something in writing from the UK side."
"We are cautiously optimistic," the diplomat said.
Pro-Brexit supporters reacted with anger to the reports, with leading campaigner Nigel Farage calling the reported 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 dispelled pro-Brexit campaign claims.
"This is a whopping great symbol for the impossibility on delivering Brexit on the terms it was sold to the British people," he told BBC Radio 4's Today programme.
Investors were more optimistic that the reports heralded a breakthrough, sending the pound 0.4 percent higher against the dollar, a two-month high.
"Let's get this show on the road," he told the BBC during a trip to the Ivory Coast.
- Irish issue -
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 future trade ties with the EU.
It would leave two major areas on which the two sides still do not agree -- expatriate citizens' rights after Brexit and the future of the Irish border.
One key area of contention is whether the 3.2 million EU citizens living in Britain will continue to be allowed to appeal to ECJ jurisdiction or if their rights will be governed by British courts, as London insists.
So far both sides have avoided publicly declaring a clear-cut number for what Britain owes the rest of the EU.
Prime Minister Theresa May had offered to cover Britain's contributions to its budget in 2019 and 2020 -- a total of around 20 billion euros.
That pledge was reportedly doubled to 40 billion euros at a ministerial meeting in London last week.
The Telegraph quoted an EU source with knowledge of the talks said the text of the financial agreement would allow a "low figure" to be generated for the British public but would also give the EU the certainty it is looking for.
Asked about the reports, a spokesman for Britain's Department for Exiting the European Union said "intensive talks" are taking place in Brussels this week, and did not address the divorce bill directly.
"We are exploring how we can continue to build on recent momentum in the talks so that together we can move the negotiations on to the next phase and discuss our future partnership," he added.
(This story has not been edited by NDTV staff and is auto-generated from a syndicated feed.)